^^;-'  :S«/^-r,.^.^-'s^ 


^w^# 


"O^^ 


University  of  California  •  Berkeley 


A  NEW  SYSTEM 

OF 

JtSERCANTIlS  ARZTHMETZq, 

ADAPTED    TO    THE 

eommetce  of  ttie  aJniteir  States, 

IN     ITS 

DOMESTIC  AND    FOREIGN  RELATIONS  : 

WITH 

FORMS  OF  ACCOUNTS, 

AND 

OTHER  WRITINGS  USUALLY  OCCURRING  IN   TRADE. 


BIT  IMIICHABZi  "V^AZiSH;  A.  M. 


ITER  EST  BREVE  PER  EXEMPLA. SENECA. 

FOURTH  EDITION. 

TO    WHICH     IS    ANNEXED    A 

SYSTEM  OF  SOOXE-KBEPIIVG. 

SALExM : 
P'UBLISHED    BY    JAMES    R.    BUFFUM,    (PROPRIETOR.) 

PRINTED    UY    JOHN     D.    CUSIimG, 

1825. 


DISTRICT  OF  MASSACHUSETTS,  to  wit : 

District  Clerk's  Office. 

BE  IT  REMEMBERED,  That  on  the  twenty  first  day  of  July,  A.  D. 
I8i4,  and  in  the  thirty  ninth  year  of  the  Independence  of  the  United 
States  of  America.  Edward  Little  &  Co.  of  the  said  district,  have  depos- 
ited in  this  office  the  title  of  a  book,  the  right  whereof  they  claim  as  pro- 
prietors, in  the  Avords  followino^,  to  wit: 

"  A  New  Sysiem  of  Mercantile  Arithmetic  :  adapted  to  the  Commerce 
of  the  United  States,  in  its  Domestic  and  Foreign  Relations  :  wiih  Forms 
of  Accounts,  and  other  Writings  usually  occurring  in  Trade.  By  Mi- 
chael Walsh,  A.  M.  Iter  est  breve  per  exempla — Seneca.  Fourth 
Edition" 

In  confonnity  to  the  act  of  the  Congress  of  the  United  States,  entitled, 
'«  An  Act  for  the  encouragement  of  learning,  by  securing  the  copies  of 
maps,  charts,  &  books,  to  the  autliors  and  proprietors  of  such  copies,  during 
the  times  therein  mentioued;"  and  al^o  to  au  act,  entitled  *'An  Act,  supple- 
mentary to  an  act,  entilled  '  An  Act  for  the  encouragement  of  learning  by 
securing  the  copies  of  maps,  charts  and  books,  'oihe  authors  and  proprie- 
tors of  such  copies  during  the  times  therein  mentioaed,  and  extending  the 
benehts  thereof  to  the  arts  of  designing,  engraving  and  etching  historical 
and  other  prints  " 

WM.  S.  SHAW. 
Clerk  of  the  District  of  Massachusetts 


Q/MOI 


RECOMMENDATIONS. 


A^ewburypnrt^  May  1 ,  1  800. 

We  the  subscribers  having  seen  Mr.  Walsh's  New  Systein  of  MER- 
CANTILE ARITHMEnO,  ami  being  satisfied  that  it  is  better  calciilat- 
ed,  than  any  yet  publishecl,  to  fit  a  youth  for  the  business  of  the  Compt- 
inii^-Ho'ise,  canno*^^  but  wish  it  an  extensive  circulation.  The  happ  elu- 
cidadon  and  extended  appiicatioii  of  the  common  rules,  together  wish  the 
many  original  improvements,  while  they  accomplish  the  student  for  com- 
merce, are  also  extremely  well  adapted  to'  assist  and  inform  the  merchanjk, 
the  mariner  and  the  trader,  in  their  variois  occupations. 
nudley  A.  Tyns,,  Mo^es  Brown, 

Ebenezer  Stoeker,  William    Wyer,jun. 

William  Bartlett,  Richard  Bartlett,jun. 

Samuel  A.   Otis,jun.  William  W.   Prout, 

Tristram  Coffin,  Michael  Little, 


Boston,  May  16,  ISOO. 
We  the  subscribers  having  examined  Mr.  Walsh's  New  Sv-stem  of 
MEROA.VTILE  ARiniMEriC,  and  being  persuaded  that  it  is  better 
calculated  than  any  we  have  met  with,  to  qualify  young  men  for  admis- 
sion into  (.'omptii^g.Hou«es,  we  wish  that  it  may  have  an  extensive  circu- 
lation. The  clear  exemplification  and  pertinent  application  of  the  com- 
mon rules,  together  wiih  the  many  useful  additions  and  improvements 
which  it  contains,  will  render  it  extremely  useful  for  the  merchant,  the 
mariner,  and  all  the  other  trading  classes  of  society. 

Marston  Watson,  John  Lowell,  jun. 

Joseph  Rii'^sell, 
Arnold  Welles,  jun 
Jonathan  Jackson: 


John  C.  Jones, 
John  Codman, 
St(*phen  Higginson, 


1  Vi^'^Hl*^  ^it.:^  X  1- 


iv  RECOMMENDATIONS. 

Salem,  October  7,  180«. 
We  the  subscribers,  merchants  of  Salem,  convinced  of  the  necessity  of 
renderi:ig  the  forms  of  business,  the  value  of  coins,  and  the  nature  of  com- 
merce, more  familiar  lo  the  United  States  as  a  commercial  people,  do  ap- 
prove of  the  MER  JANTILE  ARITHMEriCof  Mr.  Walsh,  and 
recommend  it  as  calculated  to  subserve  in  ihe  best  manner  the  instruction 
of  our  youth,  and  the  purposes  of  a  well  informed  merchant. 


William  Grayyjun. 
JBenj.  Hodges, 
Benj.  Pickf?ian, 
JYaih.  Bow  ditch  J 


Jacob  Ashton, 
TVm.  Prescott, 
Jacob  Crowninshield, 
Elias  Basket  Derby» 


PREFACE 

TO  THE  THIRD  EDITION. 

The  merit  of  Walsh's  Mercantile  Arithmetic 
having  been  submitted  to  the  public,  and  estab- 
lished by  the  most  liberal  and  unequivocal  en- 
couragement, the  Editor  feels  a  confidence  in 
offering  a  third  edition  of  ten  thousand  copies. 

It  is  unnecessary  now  to  urge  the  superiority 
of  this  over  every  similar  production  extant. 
The  discernment  of  men  of  letters,  and  the  gen- 
erous spirit  of  a  commercial  public,  have  render- 
ed panegyric  useless  by  an  unprecedented  pat- 
ronage. In  the  very  short  period  of  its  exis- 
tence two  extensive  impressions  have  been  cir- 
culated through  the  country,  and  orders  are  al- 
ready received  for  a  very  large  proportion  of 
the  third. 

Tlie  value  of  any  work  must  be  decided  by 
those  to  whom  it  is  more  immediately  useful : 
and  if  such  persons  possess  the  means  of  dis- 
crimination, the  decision  will  undoubtedly  be 
correct.  The  present  publication  is  adapted  as 
well  to  assist  the  researches  of  Mathematicians, 
as   to   facilitate  the  negociations  of  Merchants^ 

A  2 


ti  PREFACE. 

Such  characters  have  supported  it  by  their  writ- 
ten approbation,  and  recommended  it  by  an  in- 
troduction into  their  own  Studies  and  Compting- 
Rooms.  Schools  and  Academies  have  made  it 
the  basis  of  a  mercantile  education,  and  it  has 
become  an  indispensable  assistant  to  every  trad- 
ing class  of  the  community. 

This  impression  has  received  several  valuable 
additions  under  the  general  head  of  Exchange, 
including  the  existing  exchange  w^ith  Antwerp, 
Trieste,  Genoa,  Venice,  Barcelona,  and  Palermo 
in  Sicily,  and  many  useful  rules  under  each  of 
these  particular  heads.  A  new  subject  is  like- 
wise added,  entitled  "  Arbitration  of  Exchange," 
the  importance  of  which  will  easily  be  seen  by 
Merchants  whose  remittances  may  travel 
through  several  countries,  and  be  liable  to  the 
rates  of  exchange  in  each. 

The  errors  of  the  last  edition  were  few  and 
unimportant.  But  to  render  the  work  perfect, 
they  have  been  minutely  considered  and  cor- 
rected. 

The  Editor  is  confident  that  the  present  edi- 
tion will  be  taken  up  with  the  same  avidity  as 
the  two  former,  and  he  assures  the  public  that 
the  work  shall  not  sulfer  either  in  accuracy  or 
beauty,  by  the  liberality  of  its  patrons. 

EDMUx\D  M,  BLUNT. 

Septemhcr^  1804. 


PREFACE 

TO  THIS  EDITION. 


There  is  subjoined  to  this  edition  an  Intro- 
duction to  Book-Keepiufr^  on  the  plan  of  R. 
Turner,  LL.D.  with  a  Waste  Book,  as  an  exam- 
ple for  practice,  corrected  and  improved,  and 
calculated  for  the  merchants  and  traders  in  the 
United  States.  Great  simplicity  has  been  used, 
in  order  that  the  learner  may  attain  to  a  clear 
view  of  the  principles  of  this  science^  in  which 
being  once  well  grounded,  he  may  apply  them 
to  the  diversified  objects  and  transactions  of 
complicated  and  extensive  commerce. 

This  treatise  has  received  the  approbation  of 
our  most  intelligent  merchants. 

It  having  been  suggested  that  an  elucidation 
of  the  most  approved  mode  of  Eook-Keeping  by 
single  entry  would  be  useful,  a  Set  of  Books  has 
been  subjoined,  in  which  the  utmost  plainness 
and  simplicity  have  been  used. 


CONTENTS. 


PAGE 

Numeration             r             -             -             -             -             -             -  1 

Simple  Addition             ..---•.  2 

«      Subtraction             "             -             -             -             -             -  S 

Multiplication             .             -             -             -             -  3 

Division             _             -             -             -             »             -  4 

Miscellaneous  Questions             .             -             -             -             -  7 

Table  of  Moaey,  Weights,  Measures,  &c.              -              -              -  7 

Compound  Addition              -              -              -              -              -  l^ 

Compound  Subtraction              -             -              -              -             -  l-^ 

Practical  Questions  in  Compound  Addition  and  Subtraction         -  l6 
Reduction              -              -             -              -              -              --i8 

To  find  the  Contents  of  Grindstones  {To  find  the  value  seepage  57)21 

Reduction  of  American  Moneys              ...             -              -  22 

Compound  Multiplication             .             -             -             -             .  30 

Bills  of  Parcels             ...              _              -              -  30^ 

Compound  Division              -              -              -              -              -              -  37 

Decimal  FracUons              -              -              -              -               -              -  40 

Decimal  Tables  of  Coins,  Weights  and  Measures              -              -  49 

The  Single  Rule  of  Three  Direct                            -              -              -  52 

Inverse  Proportion              -              -              -              -              -              -  60 

Compound  Proportion             -             -             -              -             -  61 

Vulgar  Fractions              -.-..-  64 

Practice              --..--.  75 

Tare  and  Tret              -«.--.  83 

Single  Fellowship             -             -             -              -              -             -  87 

Dotible  Fellowship             -             -             -             -             -             -  88 

Simple  Interest              -              _              -              .              -  89 
Rule  established  by  the  Courts  of  Law  in  Massachusetts  for  mak- 
ing up  judi^ents  on  securities  for  money,  which  r.reupoo  in- 
terest and  on  which  partial  payments  have  been  endorsed  104 
A  Table  shewing  the  number  of  days,  from  any  day  in  any  month, 

to  "he  same  day  in  any  other  month  through  the  year              -  J  05 

Compound  Interest              -              -              -              -             -              -  106 

Table  shewing  the  amount  of  one  pound  or  one  dollar  for  ahy 
number  of  years  under  33  at  the  rates  of  5  and  6  per  cent,  per 

■annum,  compound  interest              -              -              -              -         -  107 

Commission  and  Brokerage             -             -             -             -         -  109 

Jiisurance  -  -  -  -  -  --111 

<*rcneial   Averajre               -              -             -             -             -           -  112 


X  CONTENTS. 

4  '       5  PASE. 

Buying  and  Selling  Stock*  -  -  -  -         -        114 

Dipcount  -  -  -  -  -^  -  -       115 

Bank  Discount  -  -  -  -*-  -  117 

Equation  of  Paj-ments  -  -  -  -  -  120 

Barter -  121 

L.O  s  and  Gain  -  -  -  -  -  -  123 

Alligation  Medial  -  -  -  -  .    -  -126 

Alligation  Alternate  -  -  -  -  -  127 

Single  Po  i  ion  ...  -  -  -     130 

Doable  Position  -  -  -  -  -  -131 

Exchange  with  Great  Britain  .  .  .  .         .     131 

Ireland  .  .  .  .  .  133^ 

Hamburgh  .  .  .  .  .       \iil 

Holland  .  .  .  .  .147 

Denmark  .  .  .  .  .  151 

Bremen  .  .  ,  .  .153 

Antwerp  ,  ,  ,  .  ,154 

Rusja  ....  156 

Fraiice  .  .  .  .  158 

Tables  for  chan|?;ing  Livres  Sols  &  Deniers,  to  Francs  &  Cen'imes       164- 
Table  for  reducing  Francs  &  Centimes  to  Livres,  Sols  &  Deniers        165 
Exchange  with  Spiin  .....  166 

Cadiz  .....  167 

BilLoa  .  .  .  .  .  172 

Barcelona  .  .  .  ,  .174 

Portu-al  .  .  .  ,  ,  .  1T# 

Leghorn  .  .  .  .  .  178 

Naples  .  .  .  .  .  181 

Triesie  .....  1S2 

Genoa  .....  184 

Venice  .  .  .  .  185 

Smyrna  .....  1^6 

Palermo  (in  Sicily)  .  .  .  ,100 

Jamaica  and  Bermudas  .  ,  .  192 

Barbidoes 194 

Maninico,  Tobago  and  St    Christopher's  .  19^ 

French  West-Indies  .  .  .  .194 

Spani-h  West  Indies  ....     198 

Calcutta  .,  ...  200 

Bombay  .  .  .  .  .  201 

Madras  .  .  .  ,  .  201 

Batavia  .  .  ...  202 

China  .  .  .    ^         .  204 

Manilla  .....  206 

Ceylon  .....  206 

Japan  .....  207 

Tonnage  of  Goods  from  the  East  Indies  to  Europe  .  208 

Arbitral  ion  4^f  Exchange  .  .  ,  .  .210 

Mode  of  Calculating  American  Duties  .  .  .  212' 


CONTENTS. 


*      -  PAGE. 

Rates  at  which   all  Foreign  Coins  are  estimated  at  the  Custom- 

Houses  of  the  Unit fd  States             .             .             .             .  215 

Aritiiine  icitl  Progresfcion  .  .  .  -  .216 

Geometrical  Progression             .             .              .             .             .  2 '  9 

Permutatiofi            ..             .              .              .              .              .              .  222 

Extraction  of  the  Square  Root             .             .             .             .  223 

Exirac'ionof  the  tube  Hoot             .....  228 

Extraction  of  the  Biquadrate  Root              .              .              .  233 

Ceueral  Rule  for  extracting  the  Roots  of  all  Powers             .  233 

Ouodecimals                          .....  235 

To  find  the  (Contents  of  Bales,  Cases,  &c  in  order  to  ascertain 

the  freight     ^     .              -              .              .              .              .  237 

To  fiiid  Ships'  Tonnage  by  (^arpenters'  Measure             .             .  238 

To  find  the  Government  Tonnage  of  Slips              .             .             .  241 

Tables  of  Cordage              .             .              ....  244 

Tablev  for  receiving  and  paying  the  Gold  Coins  of  G.  Britain,  &c.  246 

Tables  for  receiving  and  paying  the  Gold  (  oins  of  France              .  247 

Tables  for  receiving  and  paying  the  Gold  Coins  of  Spain,  &c.  248 

Mercantile  Precedents             .              ...              .             .  249 

Bill  of  Exchange              .             .              .              .              .             .  249 

Bill  of  Goods  at  an  Advance  on  the  Sterling  Cost             ,             .  249 

Promi'sory  Note              .              .             .             .             .             .  2.30 

Receipt  for  an  Endorsement  on  a  No!  e             .              ,              .  250 

Receipt  for  Money  received  on  Account              ,             .             .  250 

Promissory  Note  by  Two  Persons             .             ,            .              .  250 

General  Receipt              ....              .             .  250 

Bill  of  Parcels              ......  251 

Invoices             .             .             •             .             .            .             .  262 

Account  of  Sales             ...              ...  254 

Accounts  C  urrent              •              .              .            .             .             .  257 

Interest  Account              ......  260 

Bill  of  Sale             .......  262 

Charter  Party  .  .  ,  .  .  .  .263 

Bill  of  Lading             -             *             -            .                          ,  264 


EXPLANATION 

OF    THE 

CHARACTERS  USED   IN  THIS  WORK. 


=  SIGNIFIES  equality,  or  equal  to:  as,  20  shillings  m  one 
pound:  that  is,  20  shilling's  are  equal  to  1  pound. 

+  S.fgnifies  more,  or  Addition  :  as,  6  +  G  =  12:  that  is,  6  ad- 
ded to  6  is  equal  to  1 2. 

—  Signifies  less,  or  Subtraction :  as,  6 — 2=4:  that  is,  6  less 
2  is  equal  to  4. 

X  Signifii'S  Multiplication:  as,  6X2  =  12:  that  is,  6  multi- 
plied by  2  iS  equal  to  I  2. 

-7-  Signifies  Division:  as,  6-i-2=3:  that  is,  6  divided  by  2 
is  equal  to  3. 

Division  is  sometimes  expressed  by  placing  the  numbers 
like  a  traction,  the  upper  figure  being  the  dividend,  and 
the  lower  the  divisor  :  thus,  ^=9  :  that  is,  54  divided 
by  6  is  equal  to  9 

:  ::  :  Proportion:  as  3 :  6  :  :  9:  18;  that  is,  as  3  is  to  6, 
so  is  9  to  18. 

^  Prefixed  to  any  numler,  signifies  that  the  square  root  of 
that  number  is  required. 

Aline  or  vinculum,  drawn  over  several  numbers,  signified, 
that  the  number^;  under  it  are  to  be  considered  Join% 
as  8-^+T=:l  ;  but  without  the  line,  8— 3-f  4=9. 


MERCANTILE  ARITHMETIC. 


Arithmetic  is  the  art  of  computing  by  numbers,  and 
has  five  principal  rules  for  this  purpose,  viz.  Numeration, 
Addition,  Subtraction,  Multiplication,  and  Division. 

NUMERATION 

Teacheth  to  express  any  proposed  number  by  these  ten 
characters,  0.  1.2.  3.  4.  5.  6.  7.  8.  9. — 0  is  called  a  cipher, 
and  the  rest  figures,  or  digits;  the  relative  value  of  which 
depends  upon  the  place  they  stand  in  when  joined  together, 
beginning  at  the  right  hand,  as  in  the  following 

TABLE. 

3       .  i     -§ 


o 


^3 


Though  the  table  consists  only  of  nine  places,  yet  it  may 
be  extended  to  more  places  at  pleasure ;  as,  after  hundreds 
of  millions,  read  thousands  of  millions,  ten  thousantJs  of  mil- 
lions, hundred  thousands  of  millions,  then  millions  of  mil- 
lions, &c. 

TO  WRITE  NUMBERS. 
Rule     Write  down  the  figures  as  their  values  are  express- 
€^5  and  supply  any  deficiency  in  the  order  with  ciphers. 

B 


SIMPLE  ADDITION. 


EXAMPLES. 

Write  down  in  proper  figures  the  following  numbers^ 

Twenty-nine, 

Two  hundred  and  forty-seven, 

Seven  thousand  nine  hundred  and  one, 

Eighty-four  thousand  three  hundred  and  twenty  nine, 

Nine  hundred  and  two  thousand  six  hundred  and  fifteen, 

Eighty-nine  millions  and  ninety, 

Four  millions  four  hundred  thousand  and  forty. 

Nine  hundred  and  nine  millions  nine  hundred  and  ninety. 

Seventy  millions  seventy  thousand  and  seventy. 


Eleven  thousand  eleven  hun- 
dred and  eleven, 
eleven  thousand         11000 
eleven  hundred  1100 

eleven  11 


Fourteen  thousand  fourteen 

hundred  and  fourteen. 

fourteen  thousand   14000 

fourteen  hundred      1400 

fourteen  14 


Total     12111 


15414 


To  express  in  words  any  number  proposed  in  figures. 

Rule.  To  the  simple  value  of  each  figure,  join  the  name 
of  its  place,  beginnmg  at  the  left  hand,  and  reading  towards 
the  right. 


EXAMPLES. 


46, 


Write  down  in  words  the  following  numbers. 
199,     2267,     86693,     289'732,      51911911,    1169990,. 
9919,     4320,     55000510. 


SIMPLE  ADDITION 

Teacheth  to  collect  numbers  of  the  same  denomination 


into  one  sum. 

EXAMPLES. 

galls. 

yds. 

bushels. 

68965 

59473 

875496 

14753 

8914 

170900 

29684 

675 

574 

57693 

29 

9 

171095 

171095 


SIMPLE  SUBTRACTION. 


17573 

18U041 

750010 

468 

4095 

31994 

57 

83 

573 

9 

7326 

74837 

As  the  mercantile  method  of  proving  addition  is  to  reckon 
downwards,  as  well  as  upwards,  the  sums  of  which  will  be 
equal^  if  the  addition  is  just,  two  spaces  are  left  for  the  work. 


SIMPLE  SUBTRACTION 

Teacheth  to   take  a  less  number  from  a  greater  of  the 
same  denomination,  and  thereby  to  show  the  difference. 


EXAMPI^S. 


From 
Take 

Rem. 

Proof 


yards. 
57468532 
26587491 

30881041 

57468532 


gallons. 
From     29689141 
Take      17938762 

Rem.     11750379 


Proof  29689141 


3.  from  924357  take  565383  Rem.  358974 


4. 
5. 
6. 
7. 
8. 


517684 
510090 
191191 
291619 
500910 


291872 

191939 

2957 

829 

15723 


225812 
318151 
188234 
290790 
485187 


SIMPLE  MULTIPLICATION 

Is  a  compendious  way  of  adding  numbers  of  the  same  name. 
Th^^  number  to  be  multiplied  is  called  the  multiplicand. 
The  II  (mber  which  multipliers  is  called  the  midtiplier. 
The  number  arismg  from  the  operation  is  called  the  product 


SIMPLE  DIVISION. 

MULTIPLICATION    TABLE. 


} 

2 

3 

4 

5 

6 

1  7 

8 

9  1 

10  1 

11 

12 

1  i 

4 

^ 

8 

10 

12 

|14 

16 

18  1 

2(^ 

22 

24 

j  3| 

^^ 

^ 

12 

15 

18 

21  1 

24 

27  1 

30  j 

33 

36 

4 

•^1 

8 

12 

1.6 

20 

24 

1  28 

32 

36  1 

40 

44 

48 

^5 

20 

25 

30 

35 

40 

45 

50  1 

55 

60 

?1 

.2 
14 

18 

24 

30 

36 

142 

48 

54 

.^0| 

66 

72 

21 

28 

35 

42 

49 

56 

63  1 

70  1 

77 

84 

,  8 

IG 

24 

32 

40 

48 

1  56 

64 

72 

80 

88 

96 

w 

18 

27 

36 

45 

54 

t63 

72 

81  1 

90 

99 

108 

10 

20 

30 

40 

50 

1  60 

po 

80 

1  90 

100 

110 

120 

1 1 

22 

33 

44 

55 

66 

1  77 

88 

99 

110  1 

121 

132 

12 

24 

36 

48 

60 

_72_ 

(84 

96 

108 

120 

132 

144 

EXAMPLES. 


Multiplicand       5965468 
Multiplier   '  2 


Product 


11930936 


4765293 
3 

14295879 


6281947 
4 

25127788 


4. 

Mult.  2658758 

by   5 

product 

1329379© 

5. 

9674372 

6 

58046232 

6. 

7689657 

7 

53827599 

7. 

2674876 

9 

24073r84 

8. 

4198543 

10 

41985430 

9. 

7491685 

11 

82408535 

10. 

2689489 

12 

32273868 

11. 

1768735 

20 

35374700 

12. 

2*891496 

400 

1156598400 

13. 

5749857 

78 

448488B46 

14. 

2653294 

872 

2313672368 

15. 

78965987 

5893 

465346561391 

16. 

562916859 

490070 

275868665090130 

SIMPLE  DIVISION 

Teacheth  to  tind  how  often  one  number  is  contained  in 
another  of  the  same  name. 


SIMPLE  DIVISION.  S 

The  number  given  to  be  divilfed,  is  called  the  dividend. 
The  niiinber  by  which  to  divide,  is  called  the  divisor. 
T  he  number  of  times  the  divisor  is  contained  in  the  divi- 
dend is  called  the  quotient. 

The  remainder^  if  there  be  any,  will  be  less  than  the  divisor. 

PROOF. 

Multiply  the  quotient  by  the  divisor ;  to  the  product  add 
the  remainder,  and  the  sum  will  be  equal  to  the  dividend,  iif 
the  work  be  right. 

EXAMPLES. 


Dividend. 
Divisor     2)694568946 

Quotient      347284473 


3)2768954584 


922984861 — 1  rem. 
3 


Proof 


694568946 


2768954584 


dividend,  quotient. 
Divisor     52)6495436(  1 249 1 2 


52 


52 


129 

249824 

104 

624560 

12 

rem. 

255 
208 

6495436 

proof. 

474 

468 

63 

52 

116 

104 

12 


B2? 


■m... 


SIMPLE  DIVISION. 


4. 

Divide   8965462 

by   6 

quotient, 
Ans.  1494243 

rem 
and  4 

6. 

3728675 

8 

466084 

3 

6. 

4654682 

9 

517186 

8 

7. 

2768967 

10 

276896 

7 

o 

1949952 

11 

177268 

4 

9. 

2968967 

12 

217413 

11 

10. 

5268794 

20 

263439 

14 

n. 

29619145 

40 

740478 

25 

12. 

419825367 

500 

839650 

367 

13. 

296876234 

64 

4638691 

10 

14. 

47989536925 

735 

65291886 

715 

15. 

26574983184 

8962 

2965296 

432 

16. 

53479689236 

7684 

6959876 

2052 

17. 

4917968967 

2359 

2084768 

1255 

18. 

3258675689 

67435 

48323 

14184 

When  the  divisor  is  a  compound  number,  that  is,  if  any  two 
figures,  being  multiplied  together,  will  make  that  number, 
then  divide  the  dividend  by  one  of  those  figures,  and  the  first 
quotient  by  the  other  figure,  and  it  will  give  the  quotient  re- 
quired. But  as  it  sometimes  happens  that  there  is  a  remain- 
der to  each  of  the  quotients,  and  neither  of  them  the  true 
one,  it  may  be  found  by  this 

Rule.  Multiply  the  first  divisor  by  the  last  remainder, 
and  to  the  product  add  the  first  remainder,  which  will  give 
the  true  one, 

EXAMPLES. 

Divide  296876234  by  64 
8)296876234 

8)37109529—2 

Quotient      4638691  and  1  X  8  +  2  =  10  remaining. 
Divide  8757635  by  28         Divide  18957492  by  42 


Quot.       312772  and  19  rem.  451368  and  36  rem. 


Divide  1571196  by  72         Divide  3751749  by  96 


Quot.        21822  aQdl2  rem.  39080  and 69     rem. 


MONEY,  WEIGHTS,  MEASURES,  &c.  nr 

MISCELLANEOUS  QUESTIONS. 

1.  Add  562163,  21964,  66321,  18536,  4340,  279  and  83 
together.  Ans.  t3(:c>686. 

2.  What  number  is  it,  which  being  added  to  'J7vk)  will 
make  110901  ?  Ans.  lOiiOvf. 

3.  General  Washington  was  born  in  the  year  1732;  how 
old  was  hii  in  17^9?  Ans.  67  years. 

4.  Add  up  twice  397,  three  times  79  1,  four  times  3176, 
five  times  15880,  six  times  95280,  and  once  333040. 

Ans.   1000000. 

5.  A  cashier  received,  viz.  four  hundred  and  nine  dollars, 
twenty  thousand  and  thirteen  dollars,  eight  thousand  five 
hundred  and  ten  dollars,  nine  hundred  and  twenty-eight  dol- 
lars; of  which  he  paid  away  fifteen  thousand  fifteen  hundred 
and  fifteen  dollars :  what  was  the  whole  sum  he  received, 
and  how  much  remains  after  deducting  the  paymtmt? 

Ans.  He  received  ^29860  and  there  remains  ^13345. 

6.  What  is  the  product  of  15927  multiplied  by  4009  ? 

Ans    63851343. 

7.  128  men  have  one  half  of  a  prize,  worth  34560  dollars, 
to  be  equally  divided  between  them :  what  is  each  man's 
part?     Ans.   135  dollars.     Prove  this  answer  to  be  right. 

8.  Three  merchants.  A,  B  and  C,  have  a  stock  of  14876 
dollars,  of  which  A  put  in  4963  dollars,  B  5188  dollars,  md  C 
the  remainder:  how  much  did  C  put  in?     Ans.  4725  dolls. 


TABLE 

OF 

MONEY,  WEIGHTS,  MEASURES,  kc. 

Federal  Money. 

10  Mills      .      -        make        -      -  1  Cent. 

10  Cents 1  Dime. 

10  Dimes,  or  100  Cents     -         .         -  l   Dollar. 

10  Dollars  -         .        „         .  1  Eagle. 


MONEY,  WEIGHTS,  MEASURES,  &c, 

English  Money. 
4  Farthings       -       -       make       -       -       1   Penny. 


12   Pence 

- 

« 

-  1 

Shilling^. 

20  Shillings 

- 

* 

- 

- 

1 

Pound. 

Pence  Table. 

Shillings 

Table. 

d. 

s.  d. 

s. 

£.  s. 

20 

are       1     8 

20 

are 

1     0 

30 

-      -     2     6 

30 

- 

- 

1    10 

40 

.      .     3     4 

40 

- 

- 

2     0 

50 

-      -     4     2 

50 

- 

- 

2   10 

60 

-.50 

60 

- 

- 

3     0 

70 

.      -     5   10 

70 

- 

- 

3   10 

80 

.      -     6     8 

80 

- 

- 

4     0 

90 

-      -     7     6 

90 

- 

- 

4   10 

100 

-      -     8     4 

100 

- 

- 

5     0 

110 

-      -     9     2 

110 

■- 

- 

5   10 

120 

-      -  10     0 

120 

- 

- 

6     0 

130 

-      -  10   10 

130 

- 

- 

6   10 

140 

.      -  11      8 

140 

- 

- 

7     0 

150 

.      -  12     6 

150 

- 

- 

7    10 

200 

•      -   16     8 

200 

- 

- 

10     0 

Troy 

Weight. 

24 

Grains 

make 

- 

1 

Pen 

nyweiffht. 

20 

Pennyweights 

- 

- 

1 

Ounce. 

12 

Ounces 

- 

- 

- 

1 

Pound. 

Note.     By  this  weight  are  weighed  jewels,  gold,  silver, 
and  liquors. 


Avoirdupois  Weight. 
make 


16  Drams  - 

16  Ounces 1 

28  Pounds 1 

4  Quarters  -         .         -         -         i 

20  Hundred  weight     -         -         -         -    1 
NoTR.     By  this  weight  are  weighed  such  commodities  as 
are  coarse  and  subject  to  waste,  and  all  metals,  except  golcj 
and  Sliver.     Oie  pound  Avoirdupois  i§  equal  to  14  «z.  1^' 
dwt.  and  15^  gr».  Troy, 


Ounce. 

Pound. 

Quarter. 

Hundred. 

Ton. 


MONEY,  WEIGHTS,  MEASURES,  &c.  9 

Apothecaries  VVkight. 

20  Grains     -         -  make         -  -      1   Scruple. 

3  Scruples         -----  1   Dram. 

8  Drams       -  -         -  -         -  -      1  Ounce. 

12  Ounces        -         -  -         -  -  i   Pound. 

Note.  Apothecaries  use  this  weight  in  compounding  their 
medicines;  but  they  buy  and  sell  their  drugs  by  Avoirdupois 
Weight. 

Cloth  Mf.asurk. 


4  Nails 

ma 

[ke          -      1 

Quarter. 

4  Quarters 

- 

1 

Yard. 

3  Quarters     - 

- 

1 

Ell  Flemish. 

5  Quarters 

- 

1 

Ell  English. 

6  Quarters     - 

- 

-      1 

Ell  French. 

Long  Measure. 

3  Barley  Corns 

make 

1   Inch. 

12  Inches 

- 

1   Foot. 

3  Feet 

- 

1   Yard. 

51  Yards,  or  161  Feet 

- 

1  Pole,  Rod  or  Perch. 

40  Poles,  or  220  Yards 

- 

1   Furlong. 

8  Furlongs 

- 

1  Mile. 

3  Miles 

- 

1  League. 

60  Geographical,  or  > 
691  Statute  Miles      S 

- 

1  Degree. 

Note.     In  this  measure,  length  only  is  considered. 

Land  or  Square  Measure. 
144  Square  Inches         make  1    Square  Foot. 

9  Feet         -         -         -         -     1   Yard. 
301  Yards,  or  >  i    d  i      i>    i        t^      , 

272I  Feet  \  '     -    '  ^   ^^^^'  ^^^"^  ^^  P^^^^' 

40  Poles  or  Perches      -         -     1   Rood. 
4  Hoods  -         -         -  1    Acre. 

Note.     This  measure  respects  length  and  breadth. 

Wink  Measure. 
2  Pints  -         -  make         -  1  Quart. 

4  Quarts 1  Gallon. 

42  Gallons 1  Tierce. 

63  Gallons 1  Hogshead. 

84  Gallons 1  Puncheon. 

2  Hogsheads  1         .         -         -  1  Pipe  or  Butt. 

2  Pipes  or   i  Hogsheads         -         -  1    Tun 
Note.     The  wme  gallon  eontams  231  cubic  mcke§. 


19 


MONEY,  WEIGHTS,  MEASURES,  &c. 


Alr  and  Befr  Measure. 


2  Pints 
4  Quarts 

8  Gallons     - 

9  Gaiions 

2  Firkins     - 

2  Kilderkins 
54  Gallons     - 

3  Barrels 


make 


1  Quart. 

1  Gallon, 

1  Firkin  of  Ale. 

1  Firkin  of  Beer. 

1  Kilderkin. 

1  Barrel, 

1  Hhd.  of  Beer. 

1  Butt. 


Note.     The  ale  gallon  contains  28^  cubic  inches. 
Cubic  or  Solid  Measure* 


make 


1  Foot. 
1  Yi^rd. 


1728  Inches 

27  Feet       - 

40  Feet  of  Round  Timber,  or  j 

50  Feet  of  Hewn  Timber 
128  Solid  Feet       - 

Note.  8  feet  in  length,  4  in  breadth,  and  4  in  height, 
making  128  solid  feet,  contain  a  cord  of  wood.  This  mea- 
sure respects  length,  breadth  and  thickness. 


1  Ton  or  Load. 
I  Cord  of  Wood. 


Dry  Measure. 

2  Pints 

make 

1  Quart. 

2  Quarts 

- 

1  Pottle. 

2  Pottles      - 

- 

1  Gallon. 

2  Gallons 

-         -         -         _ 

1  Peck. 

•4  Pecks       - 

-         -         - 

1  Bushel. 

2  Bushels 

-         »         -         - 

1  Strike. 

4  Bushels 

. . 

1  Coom. 

8  Bushels       - 

-         -         -         - 

1  Quarter. 

36  Bushels 

-         -         -         - 

1  Chaldron. 

5  Quarters    - 

- 

1  Wey. 

2  VVeys      - 

. 

1  Last. 

Note.  The  gallon,  dry  measure,  contains  268J  cubic  inchei- 

Time. 

60  Seconds         -        -     make         -        -       1  Minute. 
60  Minutes     -       -          -           -  -  1  Hour. 

24  hours           -         -           -          -  -        1  Day. 

365  Pays 1  Year. 

Note.     365  days,  5  hours,  48  minutes,  57  seconds,  make 
a  solar  year,  according  to  the  most  exact  observation. 


COMPOUND  ADDITION.  11 

The  number  of  days  in  eacL  tnuuih  Ls  thus  found: 

Thirty  dixys  hath  September, 

April,  June.  an»l  Nou!mI>er; 

February  hath  menty-eight  alone, 

And  all  the  rest  have  thirty  one. 
When  the  year  can  be  divided  by  4  w  thout  a  remainder, 
it  is  Bissextile  or  Leap  Year,  in  which  February  hath  29  days. 


COMPOUND  ADDITION 

Teacheth  to  collect  numbers  of  different  denominations 
into  one  total. 

Federal  Money. 

dlb.     ctS'  m.  dlls.  cts.  m. 

r/4     71     3  396  14  4 

198      19     3  147  19  5 

157      14     4  149  57  9 

196     76     9  157  83  8 


English  Money. 

JE.  s. 

d. 

£. 

s. 

d. 

149  14 

H 

814 

16 

6^ 

387   19 

Bi 

198 

18 

H 

259  -  16 

H 

376 

14 

9^ 

874   17 

H 

226 

16 

7f 

678  15 

H 

174 

17 

lOi 

Troy  Weight. 

lb. 

oz.  dwt. 

gr- 

lb. 

oz. 

dwt. 

gr- 

48 

7   14 

id 

83 

11 

15 

22 

95 

4  17 

22 

15 

6 

16 

19 

27 

5  14 

15 

21 

8 

19 

23 

65 

0   19 

16 

33 

9 

15 

14 

19 

6   13 

15 

46 

4 

13 

17 

12  COMPOUND  ADDITION. 

AvoiHDUPOis  Weight. 
ton.  cwt.  qr.    lb.     oz.     dr.  cwt.    qr.    lb. 


18 

17 

1 

4 

13 

13 

36 

15 

3 

16 

13 

15 

29 

15 

2 

19 

12 

13 

14 

16 

3 

27 

14 

12 

16 

19 

2 

25 

13 

10 

57 

17. 

1 

14 

15 

9 

593 

1 

19 

187 

3 

19 

159 

2 

25 

283 

3 

13 

146 

2 

18 

259 

1 

22 

Apothf;caf\ies  Weight. 


lb. 

oz. 

dr. 

sc. 

gr. 

lb. 

oz. 

6^r. 

sc. 

^r. 

3 

7 

5 

1 

17 

2 

5 

3 

2 

11 

1 

3 

2 

2 

13 

1 

2 

2 

1 

14 

2 

5 

3 

2 

14 

3 

3 

5 

2 

13 

5 

4 

2 

1 

15 

5 

5 

4 

1 

12 

5 

2 

2 

2 

17 

2 

9 

3 

2 

15^ 

2 

3 

1 

2 

18 

I 

0 

4 

2 

17 

Cloth  Measure. 


yd. 
571 

qr.^nl 
1   3 

e.Jl.    qr    nl. 
873  2  3 

181 

qr. 

2 

2 

e.e. 
56 

qr. 
1 

2 

184 

2  2 

196   2  2 

196 

3 

3 

19 

2 

3 

196 

2  3 

158   1   1 

157 

4 

2 

14 

3 

2 

283 

3  2 

147  2  3 

168 

3 

3 

26 

4 

3 

146 

2  3 

326  2  2 

193 

5 

2 

83 

2 

2 

375 

3  2 

194  2  1 

214 

2 

3 

57 

3 

3 

"" 

Wine  Measure. 

*""""■ 

""*" 

" 

187 

hhd, 

1 

.  gall.  qt.  pt. 
17  3   1 

ton. 
176 

3 

.^a//  qt.  pt. 
16   2   1 

56 

3 

15  2   1 

59 

2 

57 

3 

9 

1 

29  3   1 

8 

3 

14 

2 

36 

2 

18  2  1 

17 

2 

19 

J 

217 

3 

57   1   1 

168 

1 

38 

2 

56 

1 

46  2   1 

25 

2 

52 

3 

COMPOUND  ADDITION  13i 

Ale  and  Beer  Measure. 
hhd.  gall  qU  pU  hhd.  gall,  qt  pt 

49     38     2     1  78     17     3     1 


38     45 

3     1 

19     16     2     1 

57     48 

2     1 

15     51     3     1 

49    -37 

1      1 

76     43     2     1 

57     26 

2     1 

23     26     3     1 

28      18 

3      1 

'  Measure. 

52     38     2     1 

Dry 

qr,  bush,^ 
57     4 

ph.  qt 
2     1 

chal.  bush.  pk.  qt 
576     31      1      3 

19     5 

3     1 

19     2/    2     2 

38     6 

2     3 

56     15     3     5 

27     7 

3     7 

26       8     2     4 

5     3 

1     4 

9       9     16 

9     2 

2     3 

14     15     2     S 

72     5 

3     2 

iNG   MeASUR' 

32     26     3     2 

Lo 

E. 

deg.    mil.  fur  I 
217      17     7 

f.po.   /t. 
19      14 

in. 

9 

be. 
1 

mil.  furl  po.  yd.  ft 
876     7      13     4     2 

733     17     4 

16      13 

3 

2 

129     6     26     2 

I 

283     53     5 

19      12 

2 

2 

167     4     19     3 

2 

346     26     6 

23     13 

4 

1 

157     3     15     2 

2 

189     32     3 

27      14 

5 

2 

280     2     27     I 

1 

176     14     2 

15     15 

6 

2 

194     5     32     2 

2 

921      15     4 

18     16 

7 

1 

176     4     18     5 

2 

Land 

Measure. 

acr.  roo 
741      1 

.  per. 
19 

acr.  roo.  per. 
870     3     19 

69     3 

29 

19     2     16 

15     2 

16 

54     3     37 

37     3 

14 

129     2     26 

16     2 

13 

187     3     14 

29     3 

27 

136     2     19 

14 


COMPOUND  SUBTRACTION. 

Time. 


yrs. 

days. 

hrs. 

min. 

sec. 

187 

149 

14 

13 

12 

146 

126 

16 

^6 

16 

69 

186 

19 

39 

19 

28 

140 

21 

46 

35 

7 

119 

22 

18 

26 

146 

146 

19 

57 

19 

yrs.  days.  hrs.  min.  se€. 

300  169  14  16  17 

19  186  17  16  16 

46  147  15  19  19 

87  196  23  46  47 

157  219  14  23  16 

46  138  15  42  13 


COMPOUND   SUBTRACTION 

Teacheth  to  find  the  inequality  between  numbers  of  di- 
vers denominations. 


Federal  Money. 
dolls,    cts,    ms.  dolls,    cts.  ms. 

From     1901     95     1  435     00     1 

Take       992     97     2  9     15     9 


English  Money. 
£        s.      d. 
From     191      11     3^ 
Take     114     16     2i 


dolls,  cts.    tn*, 
170     10     3 
9     50     2 


s. 


304     1 9     81 


From     389     18     Oi 
Take         9     19     4 


126 

16 

H 

100 

n 

0 
11 

5 

2f 

Troy  Weight. 


Ihs.  oz.  dwt.  grs. 
From  87  11  11  13 
Take  19  11   14  22 


lbs.  oz.  dwt.  grs, 
27  10  \h  22 
15   9   16  23 


COMPOUND    SUBTRACTION 

Avoirdupois    Weight. 

ton.  cwt.  qr.  lb.  oz.  dr. 
From  100  10  1  11  14  13 
Take       16     13     1     18     12     15 


16 


ewt.  qr.  lb. 
69  1  11 
19     3     27 


lb.  02.  dr.  sc.  gr. 
From  2  3  4  1  13 
Take     1     7     6     2     10 


Apothecaries  Weight. 

lb.  oz.  dr.  sc.  gr. 

2      1      3      1  15 

1     4     2     2  17 


yd.  qr.  n. 
From  251  1  2 
Take  127     3    3 


Cloth    Measure. 

elljl.  qr.  n.     ell  eng.  qr.  n.  ellfr.  qr.  n. 

189     2     1          419     13  389    2    2 

120    2    2          174    3    2  189    5    3 


Wine  Measure. 

tun.  hhd.  gall.  qt.  pt. 
From  591  1  13  1  1 
Take     126     2     56     3     1 


tun.  hhd.  gall.  qt.  pt. 
800  1  50  2  1 
149     2     61      3     1 


Ale  and  Beer  Measure. 

hhd.  gall.  qt.  pt.  hhd.  gall.  qt.  pt. 

From     571      19     3     1  100     36     2  1 

Take     198     53     2     1  9     27     3  1 


Dry  Measure. 
qr.  bu.  gall.  qt.  chald.  bu.  gall.  qt. 

From     38     4     5     3  69     21      3     2 

Take      17     5     1      2  49     33     5     3 


Long  Measure. 
deg.    m.  furl.  p.      f.    in.     b. 
From     819      13      1      19      11      3      1 
Take     lo;i      i'j     2     27      16     8     2 


m.  furl.  p.  f. 
219  3  14  11 
209     7      15      12 


COMPOUND  SUBTRACTION. 

Land  Measure. 


acr.  TOO.  per. 
From     591      1      U 
Take     129     3     15 


50 i   3   13 
190  2  21 


Time. 
yrs,      da.     hr.     m.     sec. 
From  171   143  11   14  19 
Take  128  174  19  51   14 


acr.  TOO.  per. 
219  2  21 
156   1   36 


yrs.  da.  hr,.  min.  sec. 
Six  ill  15  23  52 
389   190  21  48  54 


PRACTICAL    qUESTfOJYS    IM    COMPOUND    ADDI^ 

tiojY  and  subtraction. 

1.  Cast  up  the  following  sums,  viz.  twenty-three  shillings 

and  Ave  pence,  one  pound  and  nine  pence,  seven  shillings 

and  eleven  pence  three  iarlhings,   twenty  pounds  thirteen 

shillings  and  nine  pence,  fifteen  pence  three  farthings. 

£      s.      d. 

1        3       5 


1 

0 

9 

0 

7 

^»? 

10 

13 

9 

0 

1 

3? 

Ans.  £23       7       U 


Proof  £23       7       ^ 

2.  Twenty  dollars  and  four  cents,  ^we  dollars  and  three 
mills,  eighty-two  cents,  six  dollars  and  ^\q  mills. 

Ans.  31  dolls,  m  cts.  8  m. 

3.  Seventy  dollars,  three  dollars  and  three  cents,  thirty- 
four  cents  and  four  mills,  eighty  dollars  and  a  half,  six  dol- 
lars and  a  quarter.  Ans.    !  60  dolls.  1 2  cts.  4  m. 

4.  Ten  pounds  and  three  pence,  forty-five  shillings  and 
ten  pence  halfpenny,  thirty-seven  shillings  and  four  pence 
three  farthings,  nine  pound^  and  three  farthings,  one  shilling 
and  six  pence  farthing,  eighty-two  shillings  and  four  pence 
half  penny.  Ans.  £  27  7  5f 


PRACTICAL  QUESTIONS.  1'^- 

5.  Thirty  dollars  six  cents  and  a  half,  Miy  three  cents  and 
three  quarters,  eleven  cents  and  a  quarter,  nine  dollars  elev- 
en cents  and  a  half,  fifty  four  cents.     Ans.  40  dolls.  37  cts. 

6.  Take  three  shillings  and  four  pence  from  one  pound 
two  shillings  and  a  penny.  Ans.   \Ss.  9d. 

7.  From  £5  2*.  id.  take  nine  shillings  and  six-pence  half- 
penny. Ans.  £4   1^2  6i 

8.  Take   twenty  shillings  and  three  farthings  from   £8. 

Ans.  £6   19   11^ 

9.  From  18  dollars  take  eight  mills 

Ans.  17  dolls.  99  cts.  2  m. 

10.  Take  53  dimes  from  53  eagles. 

Ans.  524  dolls.  7  dimes  or  70  cts. 

1 1 .  A  merchant  bought  1 1 2  bars  of  iron,  weighing  56  cwt. 
1  qr.  11  lb.  of  which  he  sold  59  bars,  weighing  29  cwt  3  qrs. 
21  lb:  how  many  bai-s  has  he  remaining,  and  what  is  the 
weight?  Ans.  53  bars,  weighing  26  cwt.  1  qr.  18  lb. 

12.  Kequired  the  total  weight  of  4  hogsheads  of  sugar, 
weighing  as  follows,  viz.  No.  1,  9  cwt.  2  qrs.  21  lb.  No.  2, 
10  cwt.  3  qrs.  23  lb.  No.  3,  3  cwt,  2  qrs.  25  lb.  No.  4,  9  cwt. 
3  qrs.  17  lb.  Ans    39  cwt.  1  qr    12  lb. 

13.  A  ropemaker  received  3  tons  15  cwt.  3  qrs.  14  lb  of 
henip  to  be  wrought,  of  which  he  delivered  in  cordage  34 
cwt.  I  qr.  22  lb  :  how  much  remains? 

Ans.  2  tons  1  cwt.  1  qr.  20  lb. 

14.  Received  57955  mills,  4953  cents,  1913  dimes,  and  45 
eagles:  required  the  total  sum? 

Ans.  748  dolls.  78  cts.  3  mills. 

15.  A  cashier  received,  viz.  one  hundred  pounds  and  nine 
pence  half-penny,  three  thousand  seven  hundred  and  lour 
pounds  ten  shillings,  twenty  thousand  and  ninety  pounds  two 
shillings  and  eleven  pence- three  farthings,  of  which  he  paid 
away  sixteen  thousand  sixteen  hundred  and  sixteen  pounds  : 
how  much  has  he  on  hand?  Ans    £6278   13  9:|^ 

113.  A  farmer  bought  three  pieces  of  land,  measuring,  viz. 
the  first  piece  21  acres  3  roods  19  poles;  the  second,  37 
acres  2  roods  29  poles;  the  th^rd,  27  acres  2  roods  25  poles; 
of  which  he  sells  15  acres. 2  roods  39  poles  :  how  much  has 
he  remaining?  Ans.  7-  acres  1  rood  34  poles. 

17.  A  has  paid  B  £9  15  6i,  £19  11  9?,  £l4  19  7^, 
and  51.9  5''/  on  account  of  a  debt  ol'  £50:  how  much  is 
there  still  unpaid?  Ans.  £2  18  9^ 

C2 


18  REDUCTION. 

REDUCTION 

Teacheth  to  change  numbers  from  one  denomination  to 
another,  without  losing  their  value. 

Rule.  When  the  Reduction  is  descending,  multiply  the 
highest  denomination  by  as  many  of  the  next  less  as  make 
one  of  the  greater,  adding  to  the  product  the  parts  of  the 
same  name,  and  so  on  to  the  last. 

When  the  Reduction  is  ascending,  divide  the  given  num- 
ber by  as  many  of  that  denommation  as  make  one  of  the 
next  higher,  and  so  on  to  the  denomination  required,  and 
the  last  quotient  with  the  several  remainders  (if  any)  will 
be  the  answer. 

The  proof  is  by  reversing  the  question. 

Federal  Money. 
1.  hi  53  dollars  how  many  mills? 
63  dolls. 
10  i      Or  decimally,  by  adding  a  cipher  for 


630  dimes. 


each  inferior  denominatiouj  thus : 


5300  cents. 
10 

dll.d.c.m. 

Ans.  53000  mills.         53,000 

2.  In  14000  mills  how  many  dollars? 

10)14000 

(      Or  decimally,  by  separating  the  hg- 

10)1400  ^ures — counting  from  the  right  to  the 

(  name  required,  thus, 

10)140 

dll.d.c.m. 

Ans.     14  dolls.  14,000 

3.  In  57935  mills  how  many  dollars  ? 

Ans.  57  dolls.  93  cents  5  mills. 

4.  How  many  eagles  in  1933  dimes  ? 

Ans.   19  eagles  3  dollars  3  dimes. 

5.  In  1290  mills  how  many  dimes? 

Ans.  12  dimes  9  cents. 

6.  How  many  cents  in  46  dollars  ?  Ans.  4600. 

7.  In  19U004  mills  how  many  dollars  ? 

Aqs.  190  dollars  4  milla. 


REDUCTION. 

19 

English  Mowey. 

1.  In  £91    11   3-J  how  many  farthings? 

20 

1831  shillings. 
12 

Proof 
4)87902 

12)21975—2 

21975  pence. 
4 

20)1831—3 

£91    11   3i 

Ans.  87902  farthings. 

2.  How  many  pounds  in  3175  farthings?  Ans.  £3  6   If 

3.  In  195.  8Jd  how  many  farthings?         Ans.  947  farth. 

4.  How  many  pounds  in  9752  pence?     Ans.  £40   12  & 

5.  In  £40  how  many  crowns  of  6*.  Id.  each  ? 

Ans.   139  crowns  and  4  shillings  and  1 1  pence. 

6.  How  many  pounds  in  493  dollars?     Ans.  £l47    iSs. 

7.  In  143  pence,  how  many  shillings  ?      Ans.   l]s.   i\d» 

8.  Reduce  38^.  4^-c^.  to  halfpence  ?    Ans.  921  halfpence. 
Prove  the  above'answers  to  be  right. 

Troy  Weight. 

1.  In  15lb.  Troy  how  many  grains?        Ans.  86400  grs. 

2.  How  many  ounces  in  5749  dwt.     Ans.  287  oz.  9  dwt. 

3.  In  11  oz.  13  dwt.  13  grs.  how  many  grains? 

Ans.  5605  grs. 

4.  How  many  grains  in  15  spoons,  each  weighing  6  dwt. 
15  grains?  Ans.  2385  grains. 

Avoirdupois  Weight. 

1.  In  19  tons  14cwt.  2  qrs.  19  lb.  11  oz.  13drs.  how  many 
drams?  Ans.  11316157  drs. 

2.  How  many  cwt.  in  9563  lb  ? 

Ans.  85  cwt.  1  qr.  15  lb. 

3.  In  13  cwt.  3  qrs.  21  lb.  how  many  pounds  ? 

Ans.  1561  lb. 

4.  How  many  mess-pieces  of  4J  lb.  and  SJ-  lb.  of  each  an 
equal  number,  in  31  cwt.  1  qr.  12  lb.  of  beef? 

Ans.  439  pieces  of  each. 

Wine  Measure. 

1.  In  25  tuns  of  wine  how  many  pints  ? 

Ans.  50400  pints«. 


20  REDUCTION. 

2.  How  many  hogsheads  in  4935  quarts  ? 

Ans.   19  hhds.  36  galls.  3  qts* 

3.  In  3  hhds.  13  galls.  2  qts.  how  many  hail' pints? 

Ans.  3240  half  pints. 

Cloth  Measure. 

1.  In  158  yards  how  many  nails?  Ans.  2528  nails. 

2.  How  many  ells  English  in  5932  nails? 

Ans.  296  ells  3  qrs. 

3.  In  29  pieces  of  holland,  each  containing  36  ells  Flem- 
ish, how  many  yards  ?  Ans.  783  yards. 

Long  Measure. 

1.  In  29  miles  how  many  inches  ?    Ans.   1837440  inches. 

2.  How  many  furlongs  in  19753  yards? 

Ans.  89  fur.  1 73  yards. 

3.  In  590057  inches  how  many  leagues  ? 

Ans.  3  ieag.  2  fur.  110  yds.  1  ft.  5  in. 

Time. 

1.  How  many  hours  in  57  years,  allowing  each  year  to  be 
365  days  6  hours  ?  Ans.  499662  hours. 

2.  In  57953  hours  how  many  weeks  ? 

Ans.  344  weeks,  6  days,  17  hours. 

3.  How  many  days  from  the   19th  of  March  to  the  23d  of 
September  followmg  ?  Ans.   188  days. 

4.  How  many  days  from  the  24th  of  May,   1797,   to   the 
15th  of  December,  1798?  Ans.  570  days. 

Land  Measure. 

1.  In  41  acres  2  roods  14  perches,  how  many  rods? 

Ans.  h654  rods  or  perches. 

2.  How  many  square  rods  in  7752  square  feet  ? 

Ans.  28  rods  129  feet. 

3.  In  5972  perches,  how  many  acres  ? 

Ans.  37  acres  1  rood  12  perches. 

Solid  Measure. 
1.   In  a  pile  of  wood  96  feet  long,  5  feet  high,  and  4  feet 
wide,  how  many  cords  ?  Ans.   1 5  cords. 

.  2.  In  82  tons  of  round  timber  how  many  incbes? 

Ans.  5667840  incbes. 
3.  What  are  the  contents  of  a  load  of  wood,  6  feet  long,  4 
feet  high,  and  2^  feet  wide  ?  Ans.  3J  feet. 


REDUCTION.  21 

Grindstones  are  sold  by  the  cable  foot,  commonly  called 
a  stone,  and  the  contents  are  thus  found  : 

Rule.  To  the  whole  diameter  add  half  of  the  diameter, 
and  mnltiply  the  sum  of  these  by  the  same  half,  and  this  pro- 
duct by  the  thickness;  divide  this  last  number  by  17!^8,  the 
inches  in  a  cubic  foot,  and  the  quotient  is  the  contents  or 
answer  required. 

EXAMPLES. 

4.  How  many  cubic  feet  in  a  grindstone,  24  inches  dia- 
meter, and  4  inches  thick  ? 

24  diameter. 
12  half  diameter. 

•36 
12 

432 

4  thickness. 

1728)1728 

Ans.      I   foot. 

5.  What  are  the  contents  of  a  grindstone,  36  inched  dia- 
meter, and  4  inches  thick  ? 

36 
18 

54 

18 

432 
54 

972 
4 

1728)3888(21 
3456 


432 
4 


1728)1728(1 

1728  Ans.  2^  cubic  feet. 


22  REDUCTION. 

AMERICAJV  MONEYS. 

To  change  New-England  and  Virginia  currency  to  Federal 
monoy,  the  dollar  being  6  shillings. 

Rule.  As  the  value  of  a  dollar  is  equal  to  three  tenths  of 
a  pound,  when  pounds  are  given  to  be  changed,  annex  three 
ciphers  to  the  sum,  and  divide  the  whole  by  3  j  the  quotient 
is  the  answer  in  cents. 

EXAMPLES. 

1.  Change  £523  to  Federal  money. 
3)523000 


2. 

184 

3. 

29 

4. 

57 

5. 

219 

6. 

81 

7. 

127 

1743331  cents.     Ans.  1743  dolls.  33^  cts. 
Change  the  following  sums,  viz. 

j£  dolls,  cts. 

Ans.  613  35^ 

96  66f 

190 

730 

270 

423  33i 

When  pounds  and  shillings  are  given,  to  the  pounds  annex 
half  f  he  number  of  shillings  and  two  cipher-*,  if  the  number 
of  shillings  In  the  given  sum  be  even  ;  bat  if  the  number  be 
odd,  anriex  naif  the  number,  and  then  5  and  one  cipher,  and 
divide  by  3  ;  the  quotient  is  the  answer  in  cents. 

PXAMPIES. 

1.  Change  £69   18^.  to  FedcriU  money. 

3)59900 

!  i*  n>C>|-  cts.   Ans.  1 99  dolls.  66|  cts. 

2.  Change  £93   )ps.  to  Federal  money. 

3;V':^«'50 
1 — m — 

3121.61  cts.  Ans.  312  dolls.  16|  cts. 

Chaftg'e  the  followmg  sums,  viz. 

£      s  flolls.  cts. 

3.  129   13         -         -         Ans.       432   16| 

4.  63   15         -         -         -  212  50 

5.  27    18  -         -         -  93 

6.  IP/^    19         -         -         -  609   83i. 

7.  57    16  -  -  -  nn:   6>j| 

8.  121     7         -         -         -  404  50 


REDUCTION.  '     23 

When  there  are  shillings,  pence,  &c.  in  the  given  sum, 
annex  ibr  the  shillings  as  belbre  directe(?,  t^tk!  to  these  add 
the  farthings  in  the  given  pence  and  farlh.rigs,  observing  to 
increaBs  their  number  by  one  when  they  exceed  12,  and  bj 
two  when  they  exceed  37,  and  divide  as  before. 

EXAMPLES. 

1.  Change  £21   8s.  4^(1.  to  Federal  money. 

3)21419  4  is  armexed  to  the  pounds  for  half  the 

shillings,  and   19  for  the  farthmgs  in 

7139|  cts.    ^d.  and  excess  of  12. 

Ans.  71  dolls.  39|  cts. 

2.  Change  £117   16^.  2d.  to  Federal  money. 

3)117808 


392691  cts.         Ans.  392  dolls.  69^  cts. 

3.  Change  £721  9*.   I  X^d.  to  Federal  money. 

3)721497  In  this  example  4  is  annexed  to  the  pounds 

for  half  the  even  shillings,   and  47  for  the 

240499  cts.       farthings  in  W^d.  and  excess  of  37,  and  then 
5  is  added  to  the   figure  next  to  half  the 
shillings,  making  it  9  in  place  of  4  for  the  odd  shilling. 

Ans.  2404  dolls.  99  cts. 

4.  Change  £  29  11   2i  to  Federal  money. 

3)29559 


9853  cts.   '        Ans.  98  dolls.  53  cts. 

Ghange  the  following  sums,  viz. 

,    dolls,    cts. 
-      Ans.  86  62*. 
81    94 
4128   46f 

8.  2001      1    3^:       -         -         -  6670  2if 

9.  153  17  6"*       -         .         -  512  91| 


£ 

's.   d. 

5. 

25 

19  9 

6. 

24 

11    7f 

7. 

1<2>38 

10  91 

24- 


REDUCTION. 


A    TABLE 

For  changing  Shillings  and  Pence  into  Cents  and  Mills* 


MIL 

skill. 

shiil. 

6kilL 

shilL 

skdl. 

0 

1 

2 

3 

4 

5 

pence. 

cts.  m 

cts    m. 

cts,  m. 

cr;y.  wi. 

cts,  m. 

cts,  m. 

0 

16  7 

33  3 

oO  0 

66  7 

83  3 

1 

1    4 

la  1 

34  7 

51   4 

68   1 

84  7 

o 

2  8 

19  5 

36   1 

52  8 

69  5 

86    1 

3 

4  2 

20  9 

37  5 

54   2 

70  9 

87   5 

4 

5  6 

22  3 

38  9 

55  6 

72  3 

88  9 

5 

7  0 

23  7 

40  3 

57  0 

73  7 

90  3 

6 

8  3 

25  0 

41    7 

58  3 

75  0 

91   7 

7 

9  7 

26  4 

43  0 

59  7 

76  4 

93  0 

8 

11    1 

27  8 

44  4 

61    I 

77  8 

94  4 

9 

12  5 

29  2 

45  8 

62  5 

79  2 

95  8 

iO 

13  9 

30  6 

47   2 

63  9 

80  6 

97  2 

Jl 

15  3 

32  0 

48  6 

65  3 

82  0 

98  6 

To  change  Federal  Money  to  JV.  England  ^  Virginia  Currency, 

RvLE.  When  the  sum  is  dollars  only,  multiply  it  by  3, 
and  double  the  first  figure  of  the  product  for  shillmgs,  and 
the  rest  of  the  product  will  be  pounds. 

When  there  are  cents  in  the  given  sum,  multiply  the  whole 
by  3,  and  cut  off'  3  figures  of  the  product  to  the  right  hand 
as  a  remamder. 

Multiply  this  remainder  by  20,  and  cut  off  as  before. 

Proceed  in  this  manner  through  the  several  parts  of  a 
pound,  and  the  numbers  standing  on  the  left  hand  make  the 
answer,  in  the  several  denominations. 

Note.  If  there  be  mills,  cut  off*  four  figures,  and  proceed 
as  above. 

EXAMPLES. 

1.  Change  872  dollars  to  New-England  currency. 
872 
3 

£        s, 

261     12  Ans.     261     12 


REDUCTION. 

25 

2.  Change  1971  dls.  96|  cts.       3.  Reduce  1259  dls.  89  cts. 

to  Massachusetts  currencj.         and  7  ms.  to' Mass.  currency. 

1971   96i                                     1259  89  7 

£ 

3                                                         3 

;591,590                                      £377,9691 

20 

20 

^.11,800 

5.19,3820 

12 

12 

c?.9,600 

eZ.4,5840 

4 

4 

/•.2,400 

/.2,3360 

Ans.  £591   11   9l                     Ans.  £377  19  4^ 

A    TABLE 

For  changing  Cents  into  Shillings^  Pence  and  Farthings, 

cts. 

Cts. 

CIS. 

cts. 

cts. 

cts. 

cts. 

cts. 

cts. 

10 

^0 

rJO 

40 

50 

60 

70 

80 

90 

cts. 

d. 

,.    d. 

s.    d. 

..      d. 

^       d. 

^.    d. 

5.      rf. 

s.    d. 

5.      c^. 

*.     (i. 

0 

7J 

<  n 

I     ^ 

2     4? 

3  0 

3     71 

4   2^ 

4     91 

5    4| 

1 

3 

4 

8 

i   3 

1    10] 

2     5^ 

3  Of 

3       8 

4  3 

4    101 

5    51 

2 

'i 

8-? 

1   S^ 

I  n 

2     6i 

3  4 

3     8| 

4  3f 

4   11 

5    61 

.3 

2} 

9i 

I  4:- 

1  'i| 

-2     7 

3  2-i 

3     91 

4  4| 

4   Uf 

5    7 

4 

n 

10 

1  ^i 

2     0.^ 

2     7| 

3  2f 

3   10 

4  51 

5     01 

5    7f 

5 

■H 

lOf 

1   6 

i      l| 

2     8J: 

3  31 

3   lOf 

4  6 

5      11 

5    81 

e; 

^ 

11} 

1    6| 

2     S 

^     9 

3  4 

3   lU 

4  6f 

5     2 

5    9 

7 

h 

1   OJ 

1   l-l 

..     2| 

2     9f 

3  5 

4     Oi 

4  71 

5     2| 

5    9f 

o 

'>-i 

1  1 

!    0 

2     3} 

2   lOf 

3  5f 

4      1 

4  8 

5     31 

5  101 

'^ 

t'l  1 

1  If 

'    ^>i 

4     4 

2  1  H 

3  61 

4      If 

4  8f 

5     4 

hi>l 

To  change  JSliw-  York  and  North-Carol ina  currency  to  Federal 

mrmey^  the  dollar  being  eight  shillings. 

Rule.     Prop  ae    the   eiveii  sum  by    the   rule   for  New- 

England  money,  and  divide  by  4 :  the  quotient  is  the  answer 

in  c 

ent 

S. 

m 

EXAMPLES. 

1.  Change  £461  to  Federal  money. 
4)461000 


115250  cts. 


Ans.  1152  dolls.  50  cts. 


D 


26  REDUCTION. 

2.  Change  £419  10*.  S^d.  to  Federal  mOney. 
4)419535 

1048831  cts.  x\ns.   1048  dolls.  83f  cts. 

To  change  Federal  money  to  JVew-York  and  North  Carolina 
currency. 
Rule.     As  for  Massachusetts  currency,  using  4  as  a  multi- 
plier instead  of  3 ;  the  value  of  a  dollar  being  equal  to  four 
tenths  of  a  pound. 

EXAMPLES. 

1.  Change  1684  dollars  to  New- York  and  North-Carolina 
currency.  1684 

4 


Ans.  £673   12 
2.  Change  1048  dolls.  83f  cents  to  New-York  currency. 
1048,831 
4 


419,535 
^0 

10,700 
12 

8,400 
4 

1,600  Ans.  £419  10^.  ^\d. 

To  change  New-Jersey^  Pennsylvania^  Delaware  and  Maryland 
currency  to  Federal  money ^  the  dollar  being  Is.  6d. 
Rule.  As  the  value  of  a  dollar  is  equal  to  f  of  a  pound, 
multiply  the  given  sum,  when  it  is  pounds  only,  by  8,  and  di- 
vide by  3,  for  dollars.  If  there  be  shillings,  kc.  increase  the 
sum  in  pence  by  ^  of  the  whole  sum  for  cents. 

EXAMPLES. 

1.  Change  £471  to  Federal  money. 
471 

8 


3)3768 
Ans.  125G  dollars. 


REDUCTION.  27 


2.  Change  £480  19s.  9d.  to  Federal  money. 
480  19  9 
20 

9619 
12 


S) 11 5437 

1282631  cents.         Ans.  1282  dolls.  63^  cts. 

To  change  Federal  money  to  JYew-Jersey^  Pennsylvania^  Dela- 
ware and  Maryland  currency. 
RuLK.  Multiply  the  sum,  when  in  dollars,  by  3,  and  di- 
vide by  8,  for  pounds.  If  there  be  dollars  and  cents,  multi- 
ply the  given  sum  by  90,  and  the  product  (rejecting  two 
figures  on  the  right)  is  pence  ;  or  deducting  yV  of  the  sum 
gives  the  pence  likewise. 

EXAMPLES. 

1.  Change  1256  itollars  to  Pennsylvania  currency. 
1256 
3 


8)3768 

Ans.  £.471 
2.  Change  1282  dolls.  63^  cts.  to  Pennsylvania  currency- 
128263^         Or  yV)< 282631 
90  12826J- 


12)115437,00  12)115437 

20)9619—9  20)9619—9 


Ans.  £480  19  9  £480  19  9  as  before. 

To  change  South-Carolina  and  Georgia    currency   to  Federal 
money^  the  dollar  kcing  4s.  Sd. 

Rule.  As  the  value  of  a  dollar  is  equal  to  ^\  of  a  pound, 
if  the  sum  be  pounds  only,  multiply  it  by  30,  and  divide  by 
7,  for  dollars.  If  there  be  shillings,  &c.  annex  two  ciphers 
to  the  pence  in  the  given  sum,  and  divide  by  56,  the  pence 
in  a  dollar,  the  quotient  is  the  answer  in  cents. 


23  REDUCTION. 

EXAMPLES. 

1 .  Change  j£28  to  Federal  money. 

28 
30 

7)840 

120  Ans.  120  dolls. 

2.  Change  £11  4  8  to  Federal  money. 

11  4  8 
20 

224 
12 


8X7=56  8)269600 

7)33700 

4814f  cts.  Ans.  48  dolls.  14fcts. 
To  cJiange  Federal  money  to  South-Carolina  and  Georgia 
currency. 
Rule.  Multiply  the  dollars  by  7,  and  divide  by  30,  for 
pounds.  If  there  be  dollars  and  cents,  multiply  by  56,  and 
the  product  (rejecting  two  figures  on  the  right)  is  the  an- 
swer in  pence.  examples. 

1.  Change  540  dolls,  to  S,  Carolina  and  Georgia  currency. 
540 
7 


3|0)378|0 


Ans.  £126 

2.  Change  48  dolls.  14f  cts.  to  South  Carolina  currency. 
4814f  56 

56  2 


28884  7)112 

24070  

16  16 


12)2696,00 
20)224—8 


114  8  Ans.  £11  4  8 


REDtfCTJON.  1^1; 

To  change  Canada  and  JVova-Scotia  currency  to  Federal  moncy.^ 
the  dollar  being  5  Shillings. 

Rule.  As  the  value  of  a  dollar  is  equal  to  one  fourth  of  a 
pound,  multiply  the  sum,  when  in  pounds,  by  1,  for  dollars. 

When  there  .are  shillings,  &c.  reduce  the  given  sum  to 
pence,  annex  2  ciphers,  and  divide  by  60,  for  cents. 

EXAMPLES. 

1.  Change  £36  Canada  currency  to  Federal  money. 

36 

Ans.  144  dolls. 

2.  Change  £528  12  6,  Canada  currency,  to  Federal 
money.  20  Or  thus,  528 


10572 


4 


12  2112 

lOshill.  ==  2 


6|0)1268700|0  2^.  6^^.  =  0  50 

211450  cts.  2114  50 

Ans.  2114  dolls.  50  cts. 

To  change  Federal  money  to  Canada  and  JVova-Scotia  currency,- 
Rule.     Divide  the  sum  in  dollars  by  4  for  pounds. 
If  there   be  dollars  and  cents,  multiply  the  given  sum  by 

60,  and  the  product  (rejecting  two    figures  on  the  right)  is 

the  answer  in  pence. 

examples. 
1.  Change  144  dollars  to  Canada  currency. 
4)144 


Ans.  £36 
2.  Change  2114  dolls.  50  cts.  to  Canada  or  Nova-Scotia 
currency.  211  450 

60 


12)126870(00      • 
2!0)1057|2— 6 

528  12  6  Ans,  £528  12  0 


30 


COMPOUND  MULTIPLICATION. 


COMPOUND  MULTIPLICATION 

Is  the  multiplying  of  numbers  of  different  denominationg 
by  a  simple  figure  or  figures,  whose  product  shall  be  equal 
to  a  proposed  number. 

I.  When  the  quantity  does  not  exceed  1 2,  multiply  the 
price  by  the  quantity,  and  the  product  will  be  the  answer. 

EXAMPLES. 

Multiply  £19I     17     8^  £913     11     9f 

by  2  5 


Ans.  £383     15     5 

£4567     19     05 

Itiply  £980     19     llf 
by                         12 

£209     18     4^ 
9 

1.  What  will  7  yards  of  shalloon  come  to  at  3s.  bd,  per 
yard?  s.    d, 

3     5 

7 


£1 

3  11 

s.   d.                        £     .. 

d. 

2. 

4  lb.  tea       - 

■       6     8       -         -          16 

8 

3. 

5  bushels  rye 

-       5     9       -         -          18 

9 

4. 

6  gallons  wine 

7     5       -         -          2     4 

6 

6. 

7  quintals  fish 

-     19     6       -         -          6  16 

6 

6. 

9  cwt.  iron 

■     29   10       .         -        13     8 

6 

7. 

1 1  gallons  brandy 

8     5-         -          4  12 

7 

8. 

1 2  quintals  fish 

22   10        -         -        13   14 

0 

11. 

If  the  number  or 

quantity  exceeds  12,  and  is 

to  be 

found 

in  the  table,  multiply  by  its  component  parts. 

EXAMPLES. 

s.     d. 

1. 

14  yards  durant  at 

2     5 

2 

4    10 

Ans.  £1 

7 

13  10 

COMPOUND  MULTIPLICATION.  31 


s- 

cZ. 

2. 

16  yards  silk,       at 

4 

9 

3. 

20  lb   cotfee 

1 

9i 

4. 

2o  g-ailons  rum 

6 

5,^ 

5. 

45  cwt-  iron 

29 

6 

6. 

56  yards  broadcloth 

28 

7 

7. 

6S  pair  shoe!* 

9 

3 

8. 

84  qui  11  ta is  tish 

18 

6 

9. 

lUO  gallons  molasses 

3 

^ 

10. 

121  bushels  corn 

4 

3 

11. 

144  gallons  brandy 

5 

•f 

£ 

#. 

d. 

3 

16 

0 

1 

15 

10 

9 

1 

5 

66 

7 

6 

80 

0 

8 

29 

2 

9 

77 

14 

0 

17 

5 

10 

25 

14 

3 

40 

13 

0 

To  multiply  by  fractional  pa  rts^  as  |,  },  J,  ^c. 

Rule.  Multiply  the  price  by  the  upper  figure  of  the  frac- 
tion, and  divide  the  product  by  the  lower,  the  quotient  will 
be  the  answer ;  but  when  the  upper  figure  is  not  more  than 
one,  dividing  the  price  or  sum  by  the  lower  figure  gives  the 
answer. 

EXAMPLES. 

1.  What  is  f  of  a  yard  of  cambrick  worth,  at  12^.  6d,  per 
yard?  12     6 

3 


8)37     6 

Ans.      4s.  Q^d. 

2.  What  is  f  of  a  yard   of  broadcloth  worth,   at  Sbs.  per 
yard  ? 

35  Or  thus,     2)35 

3 


4)105 
Ans.      26^.  Sd, 


2)17  6  price  of  half  a  yard* 
8  9  price  of  a  quarter. 


26  8 

3.  One  quarter  of  a  yard  of  fine  linen,  at  7^.  6d.  per  yard. 

4)7     6 

1   10J  Ans.  1^.  lO^df. 

4.  Multiply  £4     5     3  by  i,  or  take  i  of  it. 

3)4     5     3 

Ans.  £18     6 


32  COMPOUND  MULTIPLICATION. 

5.  Multiply  £9  6^.  Sd.  by  |,  or  tak^  f  of  it 
9     6     8 

7 


8)65     6     8 

Ans.     £8     3     4 

III.  When  the  number  does  not  exceed  the  table,  and  it^ 
cannot   be  found  in  it,  find  the   nearest  to  it,   either  less  or 
greater;  then,  after  having  found  the  price  of  this  number, 
add  or  subtract  the  value  of  so  many,  as  it  is  less  or  greater 
than  the  given  number. 

EXAMPLES. 


1. 

37  bushels  corn,  at  4*.  l\d.  per  bushel. 
4   11 
G 

1 

9     6 
6 

8 

17     0  price  of  36  bushels. 
4  11  price  of    1  bushel. 

2. 
3. 
4. 
b. 
6. 
7. 

Ans.    £9     111   price  of  37  bushels. 

s.    d.        ^          £     s, 
171  yards  of  shalloon,  at  2     8             Ans.  2     6 
23|  lb.  coffee,                     1    10^                    2     4 
bl\  gallons  rum,                4     2}                   12     1 
87J  yards  baize,                2     1                        9     2 
109    quintals  fish,              14     6                     79     0 
1371  gallons  molasses,         3     8i                   25     6 

d. 
0 

6 
1^- 

fV".  When  the  number  is  above  the  table,  find  the  price 
of  each  figure,  as  in  the  following : 


COMPOUND  MULTIPLICATION.  33 


EXAMPLES. 


178  yards  of  muslin  at  4^.  bd.  per  yard. 
4     5 
10 


2     4     2 
10 


22     1     8  price  of  100  yards. 
15     9     2  price  of    70 
115     4  price  of      8 


Ans.  £39     6     2  price  of  178  yards. 
2.  284  J  gallons  of  molasses,  at  3s.  9^d.  per  gallon. 


3     9^ 
10 


1 

17 

11 
10 

18 

19 

2 
2 

37   18  4     price  of  200  gallons. 

15     3  4     price  of    80 

15  2     price  of      4 

1  lOJ    price  of       ± 

Ans.  £53  18     8|  price  of  284  ^  gallons. 

s.    d.  £    s.  d, 

3.  183  gallons  gin,     at       7     5         Ans.     67  17  3 

4.  346  quintals  fish,    -       23     9  -      409   13  9 

5.  769|  lb.  coffee        -         1    10  -        70  11  2^ 

6.  809^  yards  baize    -        2     1^         -        86     0  2i 

7.  2375^  galls,  of  molasses  3     5J         -      410  15     3J 

8.  Three  barrels  of  N.  E.  rum,  containing  31,  32|,  and 
33i  gallons,  at  45.  l\d.  per  gallon.  Ans.  £22  7  5^. 

9.  Four  hogsheads  of  molasses,  containing  97^,  99  j,  105^ 
and  111  J  gallons,  at  3^.  8|fl^.  per  gallon,  are  delivered  by  A 
to  B,  to  whom  he  owed  258  dollars.  It  is  required  to  know 
the  balance,  and  in  whose  favour  it  is  ? 

Ans.  4^.   1  ^ci.  in  favour  of  B. 


34  COMPOUND  MULTIPLICATION. 

When  the  amount  of  a  cvvt  is  required  at  a  certain  rate 
per  lb. 

Rule.  Find  the  price  of  one  or  two  quarters,  and  multi- 
ply the  product  by  the  component  parts  of  a  cwt. 

EXAMPLES. 

1.  1  cwt.  of  flour,  at  3c?.  per  lb. 
3 

7 

1     9 


14     0  price  of  two  quarters. 
2 


Ans.  £l     8     0  price  of  one  cwt. 
Or  by  inverting  the  question  thus, 

9     4  the  price  of  112  lb.  at  Id.  per  lb. 


£\     8     0  the  price 

of  112  lb.  at  3c^.  per 

lb 

2.     2  cwt.  flour     - 

2id.  per  lb.     - 

£2     6 

s 

3.     3  cwtr  rice 

2f           -         - 

3  17 

0 

4.     4  cwt.  iron 

31           -         - 

6     1 

4 

5.     5  cwt.  indigo 

8*.   11| 

250  le 

8 

1.  What  will  40U0  feet  of  boards  come  to  at  38^.  4d.  per 
thousand?  1      18     4 

4  m 


Ans.  £l     13     4 
2.  3596  feet  of  boards  at  365.  per  thousand. 

3596     In  this  example  three  figures  are  pointed  off 
36     as  a  remainder,  and  the  fourth  figure  of  the 

product  of  this  remainder,  multiplied  by  12, 

21576     is  set  down  for  pence.     The  fourth  figure 

10788       of  the  product  of  the  last  remainder  multi- 

plied  by  4  gives  the  farthings. 

12M,4  ^i'. 


Ans.  £6     9     51 


COMPOUNn  MULTIPLTCATION.  35 

853  feet  of  boards  at  305.  per  thousand. 
853 
30 


25,5905. 

Ans.  £15  7 

4.  3231  feet  of  3  inch.  W.  0.  plank  225^. 

5.  8637                2i           -         -             IdO;?. 

6.  960               2             -         -            1005. 

7.  888               ^         pine,                IOO5. 

£36     6  11^ 
64    15     6i 
4   16     0 
4     8     9^ 

Plank  are  sold  per  thousand  of  2^  inches,  th^  usual  thick- 
ness for  planking  vessels ;  and  as  there  are  generall}'  other 
dimensions,  as  2  and  3  inches,  the  price  of  each  is  regulated 
hy  the  price  of  the  i?|,  adding  to  it.  or  subtracting  from  it, 
in  such  proportion  as  may  be  agreed  on  wheu  purchasing. 
In  the  above  example,  taken  from  an  actual  sale,  I  of  1 5O5. 
was  added  to  it,  for  the.  three  inch,  and  i  deducted  from  it, 
for  the  two  inch,  making  the  three  inch  2255.  and  the  two 
inch  IOO5.  per  thousand. 


WEIGHTS  AND  MEASURES, 

lb,  oz.  dwt.  grs.  lb.     oz.  dwt.  grs. 

Multiply     14     9     14     17  825     8     19     2§ 

by  5  8 


Product     74     0     13  13           6605  11  19  8 

ton.  cwt.  qrs.  lb,  cwt.  qr.    lb.  oz.  drs. 

19     17     3     25  17     1      14  11  14 

9  7 


tun.  hhd.  gal. 

87     1      57 

5 


tun. 

P- 

hfid. 

gal. 

28 

1 

1 

62 

7 

What  is  the  weight  of  47  casks  of  rice,  each  weighing 
2  cwt.  1  qr.  23  lb.  ?  Ans.   115  cwt.  1  qr.  17  lb. 


36 


COMPOUND  MULTIPLICATlOlSr. 


BILLS  OF  F 

Mr,  George  Rowk  bought  of  Wii 

s. 
8  pair  worsted  hose     at     4 

5  do.    thread     do           -     3 

3  yards  kerseymere       -  14 

6  do  muslin           -         -     4 
2  do.  tammy           -        -     1 

4  shawls        -         -         -     7 

'ARCELS. 

Boston^ 

.LIAM  RUSSEI 

d. 

6       -       . 

2       -       - 

0     -     . 

2       -       - 
8       -       - 
6       -       - 

June  28, 

£\ 

0 
2 
1 
0 
1 

1804. 

16       0 
15     10 

2  0 
5       0 

3  4 
10       2 

£7 

12       2 

25  dolls 

.  36  cts. 

Portsmouth.,  \ 9th  May ^  IS04, 
Mr.  Thomas  Barrington  bought  of  Simon  Wilson, 


If  lb.  tea, 
4^  bushels  corn 
6    quarts  brandy 
6    do.        rum 
7A  yards  chintz 

4  6 

5  4 

8     4  per  ga 
7     6         do 
2     5 

SaU 

LeMUKL  KlNG^ 

No.  1,  at  4 

2,  5 

3,  5 
9,      10 

10,  11 

11,  12 
K     12,      14 

-         £0     T     lOi 
illon 

£3  11       0| 

r.  Amos  Giles  bought  of  ] 
10  boys'  coloured  hats, 
12                 do. 

4                 do. 

4                 do. 

4                 do. 

6                 do,  • 

6  men's  plain  black  do 

1 1  dolls.  84i  cts. 
^,  23d  May ^  1804. 

6       -        £2     5     0 

0       - 

6       - 

0       - 

0       - 

0       - 

0       - 

£18     7     0 
Trunk     1     4     0 

£19    11     0 

65  dolls.  16|  cts. 

COMPOUND  DIVISION.  3 

Boston^  I Oih  Au^ust^  1 803. 
Mr.  Nathan  Perkins  bought  o/ George  Allen, 

641-  yards  striped  nankins,  at     2^.       "  £6     9     0 

32  ells  mode,         -  -         3^. 

28JL  yards  calico,  -  -25.  4d. 
2"  gross  gilt  coat  buttons,  \us.  6c/. 
3    pieces  russel,         -  34s. 

£21    10     6 


71  dolls.  75  cts. 
JVezvburyport^  Sept.  10,  1803. 

Mr.  William  Sands  bought  of  Stephen  Nowland, 

2    pieces  muslin,  at  30^.  £3     0     0 

25    yards  Irish  linen, 
28-J    do,     stormont  calico, 
28^    do.     red  do. 

1  pi?ce  durant  do. 

2  pieces  blue  shalloon, 
501.  yards  dimity, 

3  pieces  persian, 


it  305. 

2s. 

.,        2.9. 

ed. 

2s. 

2d. 

565. 

575. 

6d. 

25. 

6d 

845. 

£39    12     3 


152  dolls.  4  cts. 
Received  payment  by  bis  note  of  tlie  above  date,  at  three 
months,  for  Stephen  Nowland^ 

Abraham  Trusts. 


COMPOUND  division 

Teacheth  to  find  how  often  one  nuruber  is  contained  In 
another,  of  different  denominations. 
examples. 
1.  Divide  £19  145.  9^0?.  by  2. 

2)19     \\     9^- 


An^'.  £9     17     4-J 

2.  Divif^e  £900   1 1    9]  by  ;^.  Ans.  £/.00  n   1  \\ 

Prove  this  answer  to  be  right. 
E 


38  COMPOUND  DIVISION. 

3.  Divide  £121   7^.  9Jc/.  by  5.      Ans.  £24     55.     e^d, 

4.  Divide  £248  95.    \^d.  by  9.     Ans.  £27   12s.      l^d, 

5.  Divide  £1057    Is.  3d.  hy  12.    Ans    £88      I5.     9}d. 
II.     If  the  divisor  exceeds  12,  and  it  be  found  in  the  table, 

divide  by  its  component  parts. 

EXAMPLES. 

1.  Divide  £278  C5.  9d.  between  15  men  equally. 

^)278     8     9 

"i^y^s  13  9 

Ans.  £6     3     9"  each. 

2.  If  20  lb.  of  indigo  cost  £7  55.   lOd.  what  is  it  per  lb.? 

Ans.  75.  o^d, 

3.  If  24  yards  of  durant  cost  625.  6d.  what  it  per  yard  ? 

Ans.  25.  l}d. 

4.  If  72  bushels  of  corn  cost  £20  95.  6d.  what  is  it  per 
bushel?  Ans.  55.  H^d. 

5.  If  108  lb.  of  tea  cost  £45  135.  6d.  what  is  1  lb   worth? 

Ans.  85.  b^d. 

6.  When  £166  135.  4d.  is  paid  for  500  gallons  of  "rum, 
what  is  it  per  gallon  ?  Ans.  65.  Sd. 

7.  If  1000  gallons  of  molasses  cost  £209  75.  6t/.  what  is 
it  per  gallon  ?  Ans.  45.  2|c?. 

III.  If  the  divisor  cannot  be  found  by  the  multiplication 
of  small  numbers,  as  in  the  preceding  examples,  divide  by  ft 
as  i;^  the  following 

EXAMPLES. 

1.  Divide  £46   I5.  lid  by  37. 

£    5.     d. 
37)46     1      11(1     4     11   An?. 
37 

9 

20 


37)181(4 
J  43 

33 
12 

37)407(11 

87 

37 

37. 


COMPOUND  DIVISION.  39 

2.  Divide  £33  13^.  S\d,  by  23.  Ans.  £l   9^.  3|c?. 

3.  If  345  quintals  offish  cost  £409  135.  9d.  how  much  is 
it  per  quintal  ?  Ans.  23*.  9c?. 

Dividing  by  fractional  parts,  as  J ,  |,  f ,  &c.  is  the  same  as 
multiplying^  by  them.  See  the  Kule  under  Case  11,  in  Com- 
pound Multiplication. 

J.  How  much  is  J  of  £91    11 5.  3d.l 
91    11   3  Or  thus    2)91    11   3 

3 


2)45  15   7 1  one  half  the  Slim. 
22  17  9 J  one  quarter. 


4)274   13  9 

Ans.  £60   13  5i 

£t)8    13  5] 

2.  Divide  £126   195.   Sfc?.  by  f .  Ans.  £101    11   7. 

3.  If  the  whole  of  a  ship  is  worth  £960,  what  is  f  worth? 

Ans.  £6U0. 

4.  Iff  of  a  ship  was  sold  for  £1056  2s.  Id.  what  was  lh% 
whole  valued  at?  Ans.  £1689   15  4. 

IV.  Having  the  price  of  a  hundred  weight,  to  know  ho^ 
much  it  is  per  pound  : 

Rule.  Find  the  price  of  1  or  2  quarters,  and  then  divide 
by  the  component  parts. 

1.  If  1  cwt.  of  steel  cost  £4  6*.  4t/.  what  is  it  per  lb.? 

4)4  6  4  Or  thus     2)4  6  4 

4)1    1   7  price  of  1  qr.  7)2  3  2    price  of  2  quarters. 
7)0  5  43  8)0  6  2 

Ans.  0  0  91  per  lb.  0  0  9i  per  lb. 

2.  If  1  cwt.  of  flour  cost  235.  4d.  what  is  it  per  lb.? 

Ans  ^d. 

o.  When  2  cwt.  of  sugar  cost  £8  175.  4c?.  what  is  it  per 
!b.?  Ans.  d^d. 

4.  If  5  cwt.  of  iron  cost  £8  155.  Od.  how  much  is  it  per 
lb.?  Ans.  33c/. 


I.  \  mate  and  3  seamen  have  to  receive  600  dollars,  for 
recapturino-  their  vessel,  of  which  the  mate  is  to  have  two 
share;^,  and  each  seaman  one  share ;  how  much  is  the  part 
of  each?  Ans.— The  matp's  part  is  240  dolls. 

and  each  seaman"*?  120. 


4t)  DECIMAL  FRACTIONS. 

2.  Capt.  M.  of  the  Jason,  meets  at  sea  with  the  wreck  of 
the  Hawk,  of  Boston,  from  which  he  takes  sundry  articles, 
which  sell  for  521  dollars  64  cents;  two  thirds  of  this  snm 
are  awarded  to  the  owners  of  the  Hawk  ;  of  the  other  third, 
the  owners  of  the  Jason  are  to  have  one  half;  and  the  re- 
mainder is  to  be  divided  between  the  captain,  mate,  and  nine 
seamen,  allowing  the  captain  three  shares,  the  mate  tivo^ 
and  the  seamen  one  share  each;  what  are  the  respective 
parts  of  those  concerned? 

dolls,  cts. 
Ans.     The  owners  of  the  Hawk,      347  76 
owners  of  the  Jason,        86  94 
captain,         -  -  18  f'\^ 

mnte,         -        -         -      12    12 
each  seaman,  *  6  21 


DECIMAL  FRACTIONS. 

A  Decimal  Fraction  is  that,  whose  denominator  is  an  unit, 
with  as  many  ciphers  annexed  to  it  as  the  numerator  has 
places,  and  is  usually  expressed  by  writing  the  numerator 
only,  with  a  point  before  it  called  the  separatrix  ;  thus,  y^^, 
r o\)  tWo?  ^re  decimal  fractions,  and  are  expressed  hy  ,5 
,25  ,125  respectively. 

The  figures  at  the  left  hand  of  the  separatrix  are  whole 
numbers;  thus  4,5  yards  is  4  yards  and  5  tenths,  or  one  half 
of  another  yard. 

Ciphers  placed  at  the  right  hand  of  decimals  make  no  al- 
teration in  their  value  ;  for  ,5  ,50  ,500,  &c.  are  decimals  of 
the  same  value,  being  each  equal  to  ^ ;  but  when  placed  at 
th^  left  hand,  the  value  of  the  fraction  is  decreased  in  a  ten- 
fold proportion;  thus  ,5  ,05  ,005,  Sac.  are  5  tenth  parts,  5 
hundredth  parts,  5  thousandth  parts,  respectively. 


DECIMAL  FRACTIONS.  41 

The  different  value  ot  figures  will  appear  plainer  by  the- 
following 

TABLE. 

INTEGERS.  DECIMALS. 


2, 

2  0  ,2 

2  0  0  ,©  2 

2  0  0  0  ,0  0  2 

20000, 0  002 

200000, 0  0002 

2000000, 0  0000 
f\   n   f\   n   n    (\   f\     n  A  rk  A  A 


From  this  table  it  appears,  that  as  whole  numbers  increase  in  a  tenfold 
proponion,  from  units  to  the  left  hand,  so  decimals  decrease  in  the  same 
proportion,  to  the  right ;  and  that  in  decimals,  as  in  whole  numbers,  the 
place  of  a  figure  determines  its  relative  value. 

ADDITION  OF  DECIMALS. 

Rule.  Place  the  given  numbers  so  that  the  decimal  points 
may  stand  directly  under  each  other,  then  add  as  in  whole 
numbers,  and  point  off  so  many  places  for  decimals  to  the 
right  as  are  equal  to  the  greatest  number  of  the  decimal 
places  in  any  of  the  given  numbers. 


EXAMPLES. 

263,51 

42,23 

2,4 

149,28 

18,47 

,5 

29.3,53 

9,3 

26,17 

181,59 

52,384 

,7 

129,4 

2,1 

5, 

1020,31  124,484  31,47 

E2 


42  DECIMAL  FRACTIOIS-S. 

Required  the  sum  of  twenty-nine  and  three  tenths,  tTn*e^ 
hundred  and  seventy- four  and  nine  millionths,  ninety-severr 
and  two  hundred  and  fifthy-three  thousandths,  three  hundred 
and  fifteen  and  four  hundredths,  twenty-seven,  one  hundred 
and  four  tenths.  Ans.  942,993009. 

Required  the  sum  of  ten  dollars  and  twenty-nine  cents, 
ninety-three  cents  and  three  mills,  nine  cents  and  6  mills, 
and  two  dollars  and  eight  mills.     Ans.  13  dolls.  32  cts.  7  ms. 

SUBTRACTIOJy  OF  DECIMALS. 

Rule.  Place  the  given  numbers  so  that  the  decimal  points' 
mny  stand  directly  under  each  other,  and  then  point  ofi'  the 
decimal  places  as  in  addition. 

EXAMPLES. 

From  219,42  87,26  67  311 

Take   184,38  19,4  9,375  11,11 


35,04  67,86  47,625  299,89 


From  two  thousand  and  sixteen  hundredths,  take  one  thou- 
sand and  four  and  four  millionths.  Ans.  990,159996. 

From  twenty-four  thousand  nine  hundred  and  nine  and  one 
tenth,  take  fourteen  thousand  and  twenty-nine  thousandths. 

Ans.   10909,071. 

Take  eighty-five  and  seven  hundred  and  thirty-seven 
thousandths  from  one  hundred.  Ans.   14,263. 

From  five  hundred  and  thirty-one  dollars  two  cents  take 
one  hundred  and  seventeen  dollars  three  cents  and  four 
mills.  Ans.  413  dolls.  98  cts.  6  ms. 

MULTIPLICATION  OF  DECIMALS. 

Multiply  exactly  as  in  whole  numbers,  and  from  the  pro- 
duct cut  off  as  many  figures  for  decimals  at  the  right  hand 
as  there  decimals  in  both  the  factors ;  but  if  the  product 
should  not  have  so  manvy  supply  the  defect  by  prefixing  ci^ 
phers. 


Decimal  fractions; 

EXAMPLES. 


4^ 


Multiply     36,5 
by     7,27 

29,831 
,952 

,29 
,029 

3,92 
196 

2555 
730 
2555 

59662 
149155 

268479 

2235 
3528 

392 

Product    265,355 

28,399112 

768,32 

Multiply     ,285 

by       ,8 

,285 
,003 

124 

,06 

Prorluct    ,2280 

,000855 

7,44 

Note.     To  multiply  defcimal  fractions  by  10,  100,  1000,  &c.  is  only 

to  remove  the  separatrix  so  many  places    towards  the  right  as  there  are 

ciphers  : 

Thus,    7,362937  ("10        \  (73,62937 

TV.T   !*-^i     u     )  100      f      .       1736,2937 
Multiply  by  ^,^^^    \     IS     l^.^^^.^ 

(iOOOo)  (73629,37 

Multiply  twenty-nine  and  three  tenths  by  seventeen. 

Ans.  498,1. 
Multiply  twenty-seven  thousandths  by  four  hundredths. 

Ans.  ,00108. 
Multiply  two  thousand  and  four  and  two  tenths  by  twenty* 
seven.  Ans.  54113,4. 

PRACTICAL  qUESTIOJVS. 

1.  How  much  will  93  yards  of  shalloon  come  to  at  53  ctV. 
p,er  vard  ?  93 

,53 

279 
465 

49,29         Ans.  49  dolls.  29  cts. 


2.  At  21  cents  9  mills  per  lb.  what  will  187  lb.  of  coffee 
come  to  ?  Ans.  40  dolls.  95  cts.  3  mills. 


44  DECIMAL  FRACTIONS. 

3.  What  will  27  cwl.  ot  iron  come  to  at  4  dollars  56  cents 
per  cwt.?  Ans.    123  doiis.  12  cts. 

4.  How    much  will  281  yards  of  tape  come  to  at  9  mills 
per  yard?  Ans.  2  dolls.  32  cts.  9  mills 

5.  What  will  371  yards  of  broadcloth  come  to  at  5  dollars 
79  cents  per  yard?  Ans.  2148  dolls.  9  cents. 

6.  How  much  will  29  J  yards  of  mode  come  to  at  75  cents^ 
per  yard?  Ans.  22  liolis.  12  cents  5  mills. 

7.  What  will  23,625  feet  of  boards  come  to  at  8  dollars  2& 
cBnts  per  m.?  23,625 

8,25 


118125 
47250 
189000 


194,90625  Ans.  194dlls.  90cts.  6ms. 


I 


8.  How  much  will  712  feet  of  boards  come  to  at  14  dol- 
lars per  thousand  ?  Ans.  9  dolls.  96  cts.  8  ms. 

9.  What  will  25,650  feet  of  clear  boards  come  to  at  17 
dolls.  50  cts.  per  thousand  ?     Ans.  448  dolls.  87  cts.  5  ms. 

(Ills,  cts*  dlls.    els.  m. 

10.  15,859  feet  clear  boards 

11.  812  do. 

12.  376  do. 

13.  31,496  merch'ble  do. 
14*        269  .  do. 

15.  4, 1 14  refuse         do. 

16.  393  maple         do. 

17.  57  mahogany 

18.  195  gallons  molasses 

19.  181)     do.       rum 

20.  243  yards  baize 

21.  197  feet  clear  boards 

divisiojY  of  decimals. 

Rule.  Divide  as  in  whole  numbers,  and  from  the  right 
hand  of  the  quotient  point  off  as  many  places  for  decimals  as 
the  decimal  plac;^,s  in  the  dividend  exceed  those  of  the  divi- 
sor*   If  the  places  of  the  quotient  are  not  so  many  as  the 


17  50  per  m. 

277 

53 

2 

14 

11 

36 

8 

12  75 

4 

79 

4 

8 

251 

96 

8 

6  75 

1 

81 

5 

3  37 

13 

86 

4 

8  per  foot 

31 

44 

32 

18 

24 

57  per  gall. 

111 

15 

93 

175 

77 

23  per  yard 

55 

89 

2  per  foot 

3 

94 

DECIMAL  FRACTIONS.  45 

i:i>Ie  requires,  supply  the  defect  hy  prefixing  ciphers.  If  at 
auY  time  there  be  a  remainder,  or  the  decJmal  places  in  the 
divisor  are  more  than  those  in  the  dividend,  cipi.ors  may  he 
annexed  to  the  dividend,  and  the  quotient  carried  to  any  de- 
gree of  exactness. 


),863972(, 
828 

009391 

EXAMPLES. 

,853)89,000(104,337, 
853 

kc 

359 
276 

837 
828 

3700 
3412 

2880 
2559 

92 
92 

3210 
2559 

6510 
5971 

539 
The  vario^is  kinds  that  ever    occur  in  division  are  inclu- 
ded in  the  following  cases,  viz. 

Divide  ,803         by         ,22  Ans.     3,65 

,803  2,2  ,365 

,803  22  ,0365 

80,3  ,22  365 

80,3  2',2  36.5 

80,3  22  3,65 

222  ,365  608,21  + 

222  3,65  60,821  + 

222  365  ,60821  + 

As  multiplying  by  10,  100,  1000,  &;c.  is  only  removing  the 
separating  point  of  the  multiplicand  so  many  places  to  the 
right  hand  as  there  are  ciphers  in  the  multiplier,  so  to  di- 
vide hy  the  s;ime  is  only  removing  the  separatnx  in  the 
same  manner  to  the  left. 


4$  DECIMAL  FRACTIONS. 

PRACTICAL  qUESTlONS, 

1.  When   butter  is  sold    at  12    cents  8  mills  per  lb.   hoW 
m^ny  lb.  ma)'  be  bought  for  224  dollars  ? 
,128)224,000(1750 
128 


960 
89G 


640 

640  ^ns.  1750  ib. 

Here  the  ciphers  annexed  to  the  dividend  being  equal  t© 
the  decimal  places  in  the  divisor,  the  quotient  is  a  whole 
number. 

2.  If  673  bushels  of  wheat  cost  786  dolls.  73  cents  7  miyjs, 
\yhat  b  it  per  bushel  ? 

673)786,737(1,16^ 
673 

1137 
678 

4G43 
4038 

6057 

6057  Ans.  1  doll.  16  cts.  9  miUs. 

in  this  example,  as  the  divisor  is  a  whole  number,  three 
places  are  pointed  off  in  the  quotient  to  equal  those  in  the 
-dividend. 

3.  If  493  yards  cost  4  dolls.  43  cents  7  mills,  what  is  it 
per  yard?  Ans.  0  mills. 

4.  if  125  gallons  of  molasses  cost  95  dollars,  what  is  1 
gallon  worth  ?  Ans.  76  cents. 

5.  If  '^05  yards  of  durant  cost  107  dollars  62^  cents,  what 
i^  It  per  yard  ?  hp%.  52^  centfe. 


DECIMAL  FRACTIONS.  47 

REDUCTIO.Y  OF  DECIMALS, 
Case  I. 

To  reduce  a  vulgar  fraction  to  its  equivalent  decimal. 
Rule.     Divide  the  numerator  by  the  denominator,  and  iJ^e 
quotient  will  be  the  decimal  required. 

EXAMPLES. 

1.  Reduce  J  to  a  decimal. 

4)3,00 

,75 

2.  What  is  the  decimal  of  |  ?  Ans.  ,5 

3.  What  is  the  decimal  of  }  ?  ,25 

4.  What  is  the  decimal  of -j\  ?  ,1S 

5.  What  is  the  decimal  of  ^J  ?  ,63 

6.  Express  J  decimally.  ^876 

Case  H. 

To  reduce  numbers  of  different  denominations  to  their  equivalent^ 
decimal  values. 
Rule  I.     Write  the  Sfiven  numbers  perpendicularly  under 
one  another  for  dividends,  proceeding  orderly  from  the  least 
to  the  greatest. 

II.  Opposite  to  each  dividend,  on  the  left  hand,  place 
such  a  number  for  a  divisor  as  will  bring  it  to  the  next  su- 
perior name,  and  draw  a  line  between  them. 

III.  Bei^in  with  the  highest,  and  vvriie  the  quotient  of  each 
divisioi^,  as  decimal  parts,  on  the  right  hand  of  the  dividend 
next  below  it,  and  the  last  quotient  will  be  the  decimal 
sought. 

EXAMPLFS. 

1.  Reduce  145.  Hd,  to  the  decimal  of  a  pound. 

4       2 
1 2        5,5 
20      14,4583 

Ans    ,7239 

2.  Reduce  15  shillings  to  the  decimal  of  a  pound.  Ans.  ,75 

3.  Reduce  3  qrs.  lo  ibs.  to  the  decimal  of  a  cwt. 

Ans.  .9107]  14- 

4.  Reduce  2  qrs   2  nails  to  the  'i^cimnl  of  a  yard.  Ans  ,GiiJ5 
Sft  Reduce  14  galls.  3  qts.  to    the  dcciniai  of  a  hog>:.<Nid. 

Ans.  ,^341-^- 


4ft  DEPIMAL  FRACTIONS. 

Ca^e  in. 

To  find  the  decimal  of  any  number  of  shillings,  pence  and  farthings 
by  inspection. 
Rule.  Wn  e  half  rlie  greatest  even  number  of  shillings  for  the  fir^ 
decimal  figure,  <;.;<!  lei  '.he  farthings  in  the  given  pence  and  farthings  pos- 
sess the  second  and  third  places  ;  observing  to  increase  the  second  place 
by  5  if  the  shillings  be  odd,  and  the  third  place  by  1,  when  the  farthings 
exceed  12,  and  by  2,  when  the>  exceed  37. 

EXAMPLES. 

•1.     Find  the  decimal  of  \3s.  9^d.  by  inspection. 
36         half  of  125. 
5       for  the  odd  shilling. 
39    farthings  in  9|cf. 
2    for  excess  of  37. 


,691 
2.  Find  by  inspection  the  decimal  of  155.  OJc^.,  9s.  3^d. 
195.  C>-pi,,  3s.^Qd.  k  2s.  uy.     Ans   ,784  ,465  ,978  ,175  ,148. 

Cask  IV. 
To  find  the  value  of  any  given  deci?nal  in  the  tenns  of  the  integer. 

Rule  1.  Multiply  the  decimal  by  the  number  of  parts  in  vhe  next 
less  dcDomination,  and  cut  off  as  many  places  for  the  remainder  so  the 
.right  hand  as  there  are  places  in  the  given  decimal. 

II.  Multiply  the  remairider  by  the  parts  in  the  next  inferior  denomi- 
nation, and  cut  off  a  remainder  as  before. 

III.  Proceed  in  this  manner  through  all  the  parts  of  the  in*e^er,  and 
tlie  several  denominations  standing  on  the  left  hand  make  the  answer. 

EXAMPLES. 

1.  Find  the  value  of  ,691  of  a  pound. 

,691 
20 


13,820 
12 

9,840 
4 


3,360  Ans.   13s.  9jci. 

2.  What  is  the  value  of  ,9  of  a  shilling?  Ans.   lU^rf. 

3.  What  is  the  value  of  ,592  of  a  cwt.  ? 

Ans.  2  qrs.  10  Ih.  4  oz.  ir^-fdrams. 

4.  What  is  the  value  of  ,258  of  a  tun  of  v/ine  ? 

Ans.   I  hhd.  2-f  galls. 

5.  What  is  the  value  of  ,1278,^  o^  n  yo.wl 

Ans.  4G  days  15  hours  57  min.  574-ser. 


49 


Decimal  Tables  of  Coin,  Wp.tGHT  and  MEA!?rRe. 


TABLE  1. 
IvvciLisH  Goi?r. 
£,   1  th^  Integer. 


19 
18 
IF 

IG 

ir, 

-4 
13 
12 

n 

10 

ptnrc 


4 

3 
2 

1__ 
farth. 
3 


1  dec. 

•y/i.  1 

1    ,95 

9 

,9 

8 

.85 

7 

.3 

6 

75 

5 

.7 

4 

,65 

3 

,6 

o 

55 

I 

.5 

dec 
.45 
,4 
,35 
.3 
."25 

.15 
1 

0, 


TABLE  IIL 
Troy   Weight, 

1  lb.  (he  Integer 


decimals. 

.020833 

,0!0'6r;6 

,0125 

,0083:13 

,004166 


dtcimul 
,00311' 
,00'^:0fU3|> 
OOiOlUi 


^TABLE  li. 

.'V.XG.  Coin.     I  shidl 

^OMG  \IicAg.     l/oo/ 

1  he     ftilpo^er. 


ence 
ar  d 
ichcs 

6 

5 

4 

3 

2 

1 

farth. 
3 
2 
1 


decimals, 

.5 

.416666 

,333333 

,25 

.166666 

,083333 


Ounces    the 
Fenct    in 

Table, 


same    as, 
tht    last] 


penny 

■  ei((ht 

10 

9 

8 

7 

6  . 

5 

4 

3 

2 

1 


i^rains. 

\2 

11 

10 

9 


decimal'. 
,041666 
,0375 
.033333 
.0-29166 

:o-5 

020833 
016666 
0125 
.008333 
_  .004166_ 

decimals. 
,002083 
001910 
,001736 
,201562 
.0;.1389 
,0U!  >15 
,001042 

.00(i^(»3 

,0006«>4 
,00052 1 
,000347 
,000173 


decimals. 
,0625 
,041666 
,020833 


1  oz.  the  Inte^^ir. 

PenuT/    wt.    the.   tame 
an   Shil/in;rg  {j^    ^/^ 
first  Table. 


grains. 

decimals. 

12 

,025 

11 

022916 

iO 

.020833 

9 

,01875 

8 

,01fi666 

7 

,014583 

grains 
6 
5 
4 
3 
2 
1 


decimals. 
,0125 
.010416 
,008333 
.00625 
,054166 
,202033 


TABLE   IV. 

Avoirdupois    VVt. 
112  lb.    the    Irifrger., 


qrs 
3 
2 
1 

ibTT 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

I 


ouncf 
8 
7 
6 
5 
4 
3 
2 
1 


3 

2 

1 


dtcimuls 

.75 

__,25 

decimal  9. 

...   25 

,116071 

,107143 

,098214 

,089-28f> 

,08^^07 

,07!42;J 

,0625 

,053571 

,044643 

.0:^5714 

.0267o'3 

,017857 

,008928 


derrmaf*. 
,0-  4164 
,003306 
,003348 
,00.7S0 
,00223^ 
.001674 
.0011:6 
,000558 


decimals 
,000418 
,000270 
,000139 


50 


Decimal  Tables  of  Coin,  Weight  and  Measure. 


TABLE  V. 

Avoirdupois   Wt. 
1  lb.  the  Integer. 


dtcimals. 

,4375 

,375 

,3125 

,25 

,1875 

,115 

,0625 


drms. 
8 
7 
6 
5 
4 

O 

2 
1 


decimals. 
,03125 
,027343 
.023457 
,019531 
,015625 
,011718 
,007812 
,003906 


TABLE  VL 
LiaTJiD  Measure. 
1  iim  the  Integer. 


1 

tals> 
100 
90 
80 
70 
60 
50 
40 
30 
20 
10 

9 

8 

7 

G 


decimals, 
,396825 
,357141 
,317460 
27 

*238005 
JPf:412 
,150730 
,119047 
,079365 
,039682 
,035714 
,031746 
,027 
,023809 


l^als. 


decimals- 
,010841 
,015873 
,011904 
,007936 
,003968 


ftnts. 
4 
3 
2 

1 


decimals. 
,001984 
,001488 
,000992 
,000496 


A  Hhd.  the  Integer. 


gals 

decimals 

30 

,476190 

20 

,317460 

10 

,158730 

9 

142857 

8 

,128694 

7 

,111111 

6 

,095238 

5 

,079365 

4 

,063492 

3 

,047619 

2 

,031746 

1 

,015873 

pints. 
3 
2 
1 


decim,als, 
,005952 
,003968 
,001684 


TABLE   VIL 

Measure, 

Liquid,  Dry. 

1  Gallon.    1  Quarter. 

fn(cger. 

pf.  I  dcctm.  I  bu. 
4  I  ,5  14 
3      I      ,375     I    3 


decim. 
,25 
,125 


bu. 


1 


qpt.  1    decim.  I  pk. 

3     I ,09375  I    3 

2     I  ,0625  I    2 

1     I  ,03125  I    1 


decim.als. 
,0234375 
,015625 
.0078125 

decimals, 
,005859 
,003906 
,001953 


I  q.pks. 

I       ^ 

I       2 

Ipfs. 
3 
12 
1 


TABLE  VIIL 

Long    Measure. 

1  Mile    the   Intej^er 


yards. 

decimals 

1000 

,568182 

900 

,511364 

800 

,454545 

700 

,397727 

600 

,340909 

500 

,284091 

400 

,T2n72 

300 

,170454 

200 

,113636 

100 

,0568.18 

90 

,051136 

80 

,045454 

70 

.039773 

60 

,034091 

50 

,028409 

40 

,022727 

30 

,017045 

20 

.011364 

10 

,005682 

9 

,005114 

51 


Dfximal  Tables  of  Coin,  Weight  and  Measure. 


\f^ 


yards. 

dtcimals 

8 

,004545 

7 

,003977 

6 

,003409 

5 

,002841 

4 

,002273 

3 

,001704 

2 

,001139 

1 

,000568 

feet. 

2 
1 


decimals. 
,0003787 
,0001894 


inch. 

decimals. 

6 

,0000947 

5 

,000079 

4 

,0000631 

3 

,0U0^.'474 

2 

,0000319 

1 

,0000158 

TABLE  IX. 
Time. 

1  Year  the  Integer. 


Monlha  flit  same  a? 
Pence  in  the  second 
Tabie. 


day* 

365 

300 

^•00 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

9 


decimals. 

UOOOOOO 
.821913 
,547945 
;2r3973 
,246575 
,219178 
,19^781 
,164383 
,136986 
,109589 
.082192 
,054794 
027397 
,024657 


lays. 
8 
7 
6 
5 
4 
3 

o 

1 


dtcimals 
,021918 
,019178 
,016438 
,013698 
,010959 
,008219 
,005479 
,002739 


1  Day  the  Integer. 


hoars. 
12 
11 
10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

min. 
30 
20 
10 

9 

8 

7 

6 

5 

4 

3 

2 

1 


decimals. 

,5 

.458333 

,416666 

,375 

,333333 

,291666 

,25 

,208333 

.166666 

,125 
083333 
041666 

decimals. 
.020833 
013888 
,006944 
,00625 
,00555 
,004861 
,004166 
003472 
,002777 
,002^)83 
,001388 
,000694 


TABLE    X. 
Cloth   Measure 

1   YarJ  the    lateger 

Quarters  the  same  as 
Table  IF. 


nails. 


decvmals. 
,125 
,0625 


TABLE  XI. 

L£AD  Weight. 

1  Father  the  Integer. 


hund 
10 
9 
8 
7 
6 
5 
4 
3 
2 
1 

qis 
2 
1_ 

'  IbT 

14 
13 
12 
11 
10 
9 


decimals. 
,512820 
.461538 
,4102J6 
,358974 
,307692 
,256410 
.205128 
,153846 
.1025  4 
■051282 
dtcimals 
025641 
,012820 


.  dtcimals. 
,0064102 
,0059523 
.0054945 

005-  366 
,0045787 
,0041208 
,0036630 

0032051 
,0027472 
,0022893 
,0018315 
,0013736 
,0009157 
,0004578 


SINGLE  RULE  OF  THREE  DIRECT. 


SINGLE  RULE  OF  THREE  DIRECT. 

The  Single  Rule  of  Three  Direct  teaches,  from  three 
Tiumhers  given,  to  find  a  fourth,  that  shall  he  in  the  same 
proportion  to  the  third  as  the  second  is  to  the  first. 

\C  more  requires  jnore^  or  less  requires  less^  the  proportion 
1?  direct. 

Rule  1.  Make  the  number  that  is  the  demand  of  the  ques- 
tion the  third  term,  the  number  that  is  of  the  same  name  or 
quality  the  first  term,  and  the  remaining  number  will  be  the 
middie  term. 

Reduce  the  first  and  third  numbers  into  the  same,  and  the 
irccond  into  the  lowest  denomination  mentioned. 

2.  Multiply  the  second  and  third  numbers  together,  and 
divide  the  product  by  the  first,  and  the  quotient  (if  there  be 
no  remamder)  is  the  answer,  or  fourth  number  required. 

If  after  division  there  be  a  remainder,  reduce  it  to  the 
next  denomination  below  that  to  which  the  second  number 
was  reduced,  and  divide  by  the  same  divisor  as  before,  and 
the  quotient  will  be  of  this  last  denomination.  Proceed 
thus  with  all  the  remainders  till  you  have  reduced  tliem  to 
the  lowest  denomination,  which  the  second  number  admits 
of,  and  the  several  quotients  taken  together  will  be  the  an- 
swer required. 

The  method  of  proof  is  by  reversing  the  question. 


EXAMPLES. 

3 .  If  2  yards  of  cloth  cost  4^.  what  will  1 25  yards  come  to  ? 
yds.     s.        yds.  yds.      £,     s-      yds. 

li'  2:4::   125  Proof.     If  125  :   1 2   10  :  :  2 

4  20 


2)500  250 
.2 


20)250 


Ans.  .£12  1©  500 


125)500(4  sliilling^. 


SINGLE  RULE  OF  THRtE  DIRECI*.  5*5 


2. 
come 

If  1  bushel  of 

itO? 

bush. 
If     1      : 

corn 

cts. 
75 

L  cost  75  cents, 

bush. 

::  257 

75 

1285 
1799 

what  will  257  bushels 

192,75  Ans.   192  dolls.  75  cts. 

3.  What  will  931  yards  of  shalloon  come  to  at  55  cts.  4 
ms.  per  yard?  -     Ans.  515  dolls.  77  cts.  4  ms. 

4.  How  many  bushels  of  wheat  at  1  doll.  12  cts.  per  bush- 
el, can  I  have  for  81  dolls.  76  cts.  Ans.  73  bushels. 

5.  What  will  94  cwt.  of  iron  come  to  at  4  dolls.  97  cts.  2 
mills  per  cwt.  ?  Ans.  467  dolls.  36  cts.  8  mills.. 

6.  What  will  349  Ifc^.  of  beef  come  to  at  2d.  per  lb.  ? 

Ans.  £2  18  2 

7.  At  3s.  per  vard  what  will  59  yards  of  cloth  come  to? 

Ans.  £8   17  0 

Prove  this  answer  to  be  right- 

8.  How  many  lbs.  of  beef  at  5  cts.  per  lb.  may  be  bought 
for  29  dolls.  85  cts.  ? 

cts.         lb.     dUs.cts. 

If    5     :     1   ::  29,85 

1 


,05)29,85 

597  Ans.  597  lbs. 

9.  How  many  hhds.  of  salt  at  4  dolls.  90  cts.  per  hhd.  cau 
I  have  for  392  dolls.  ?  Ans.  80  hhds. 

10.  How  manv  lbs.  of  cofiec,  at  Is.  Id.  per  lb.  mav  be 

bought  for  £8  12  7  ?  Ans.  109  lbs. 

F2 


U  .         SINGLE  RULE  OF  '1  HREE  DIRECT. 

1 1 .  When  25  yds.  of  cloth  cost  £2  12  U  what  is  it  per  yrl.? 
yds.        £   s.  d.       yd. 


If    25     :     2   12   1    ::   I 

20 

52 

12 

'» 

625 

^ 

1 

25)625(12125 
50         — 

2s.  Id. 

125 

125 

Ans.  2s.  Id. 

12.  If  56  bushels  of  corn  cost  42  dolls.  56  cts.  what  is  it 

per  bu«hcl  ? 

bush.       dlls.cts. 

bush. 

If    56     :     42,56 

::   1 

1 

56)42,56(, 
392 

76 

336 

336 

Ans.  76  cts. 

13.  If  1  Albs,  of  beef  cost  \2s.  Sd  what  is  it  per  lb.  ? 

Ans.  2  pence. 

14.  If  G73  bushels  of  rye  cost  769  dolls.  23  cts.  9  ms.  what 
h  I  bushel  worth  ?  Ans.   1  doll.  1 4  cts.  3  ms. 

15.  What   is  1  yard  of  baize  worth  when  97  yards  cost 
£l0   12^.  2icZ.  Ans.  2^.  2id. 

]C,  When  iron  is  sold  at  5  dolls.  4  cts.  per  cwt.  what  is  it 
per  ib.?  Ans.  4  cts.  5  mills. 

17.  If  891  gallons  of  molasses  cost  £l76  Gs.   lO^d.  what 
is  it  per  gallon?  Ans.  35.   llJrA 

Prove  this  answer  to  be  ri^ht. 

18.  What  w^iil  253  quintal?  offish  come  to  at  17^.  Gd.  per 
fjulntcil?  Ans.  £221   Is.  (jd< 


SINGLE  RULE  OF  THREE  DIRECT.  5 

19.  At  5  doils.  60  cts.  per  tbout-anci,  wljat  will  37  thonsanti 
of  boards  come  to  ?  Ans.  203  dolls.  50  cis. 

20  What  will  4  hhds.  of  rum  come  to,  containinp:  v«z.  79  J-, 
84,  104,  and  1 12  galls,  at  G^.  9<r/.  pergail.  ?     Ans.  Jt;i27  4  9. 

21.  What  will  327  hhds.  pf  salt  come  to  at  5  dolls.  25.  cts. 
perhhd?      -  Ans.   [7 16  dolls.  75  cts. 

22  If  3  and  4  make  9,  how  many  will  6  and  8  make? 

Ans.    18. 

23  If  a  chest  of  hyson  tea,  weighing  79  lb.  neat,  cost 
£3i   Ws.  9d.  what  IS  It  per  lb?  Ans.  ?>s.  3d. 

24.  B  ow6s  £2119  lis.  Gd.  and  he  is  worth  but£l324 
18^.  b^d.;  if  he  delivers  this  tO  his  creditors,  how  much  do 
they  receive  on  the  pound  ?  Ans.   12^.  Gd. 

25.  A  owes  B  £569  6s.  8<i.  but  failing  in  trade,  he  is  able 
to  pay  but  lbs.  Gd.  on  the  pound  :  how  much  is  B  to  rcceivej 
and  wkit  is  his  loss?        Ans.   Me  is  to  receive  £441  4  8 

His  loss  is     -     -      128  2  0 

26.  A  merchant  failing  in  trade,  owes  in  all  29475  dolls, 
tind  delivers  up  his  whole  property,  worth  21894  dolls.  3  cts. : 
how  much  per  ct.  does  he  pay,  and  what  isB's  loss,  to  whom 
he  owed  325  dolls?  Ans.  He  pays  74  dolls.  28  cts.  per  ct. 
and  B  loses  83  dolls.  59  cts. 

27.  How  much  will  4  cwt.  1    qr.  19  lb.  of  butter  come  (© 


9c/.  per  lb. 

lb. 

400=4  hundred. 
48=excess,  12  per  ct. 
28=1   quarter. 
19 

lb. 

d. 

If     1      : 

:     9  : 

:  495 

12)4455 
20)371   3 

Ans.  £18  11^.  3d. 

28.  If  3  qrs.  20  lb.  of  steel  coA  13  dolls.  20  cts.  what  is  it 
per  pound?  Ans.  12  cents, 


56  SINGLE  RULE  OF  THREE  DIRECT. 

29.  If  J  6  cwt.  3  qrs.  of  steel  cost  157  dolls.  45  cts.  what 
is  1  qr.  worth  ?  Ans.  2  dolls.  35  cts. 

Prove  this  answer  to  be  right. 

30.  A  captain  of  a  ship  is  provided  with  18000  lb.  of  bread 
for  150  seamen,  of  which  each  man  eats  4  lb.  per  week,  how 
long  will  it  last  them  ?  Ans.  30  weeks. 

31.  How  long  would  2295  lb.  of  beef  last  for  45  seamen? 
if  they  get  lib.  each,  and  that  three  times  a  week? 

Ans.   17  weeks. 

32.  Suppose  120  seamen  are  provided  with  7200  gallons 
of  water  for  a  cruise  of  4  months,  each  month  30  days;  how 
much  is  each  man's  share  per  day  ?  Ans.  2  quarts. 

33.  A  ship's  company  of  1 6  men  is  on  an  allowance  of  6 
ounces  of  bread  per  day,  when  meeting  with  a  vessel  from 
which  they  are  supplied  with  2  cwt.  of  bread ;  what  addition 
w^ill  this  make  to  their  daily  allowance,  if  they  suppose  their 
voyage  to  last  28  days  ?  '   Ans.  8  ounces. 

34.  If  17  tuns  2  hhds.  of  wine  cost  5468  dolls.  40  cts.  how 
much  is  one  pint  worth  ?  Ans.   1 5  cts.  5  ms. 

35.  How  much  will  4  pieces  of  linen,  containing,  viz.  35|, 
g6,  37^,  and  38  yards  come  to,  at  79  cts.  per  yard? 

Ans.   116  dolls.  13  cts. 

36.  How  many  crowns  of  110  cents  each  will  pay  a  debt 
of£  82   165.  l^d.  Ans.  251  crowns. 

37.  If  203  tons  9  cwt.  3  qrs.  3  lb.  of  tallow  cost  £4568 
35.  Od.  what  does  1  ton  cost.  Ans.  £22  8  0 

38.  How  many  cwt.  of  rice  may  be  bought  for  487  dolls. 
50  cts.  when  7  lb.  cost  25  cts  ?     Ans.   m  cwt.  3  qrs.  14  lb. 

39.  When  9  dolls.  36  cts.  is  paid  for  2  qrs.  22  lb.  of  sugar, 
what  is  7  lb.  worth?  Ans.  84  cents. 

40.  When  47  cwt.  3  qrs.  of  sugar  cost  £182  45.  1  \d.  what 
is  1  qr.  worth?         ^  Ans.  195.   Id. 

41.  If  6  lb.  6  oz.  Avoirdupois  cost  5  dolls.  10  cts  what  is 
it  per  ounce  ?  Ans.  5  cents. 

42.  Bought  40  tubs  of  butter  weighing  36  cwt.  2  qrs.  14 
lb.  neat,  for  472  dolls.  2  cts. ;  paid  cooperage  12  cts.  per  tub  ; 
salt  and  labour  4  dolls.  83  cts.  8  mills;  storage  6  dolls.  48 
cts. — I  would  know  what  it  stands  me  in  per  lb.  ? 

Ans,  1 1  cents  9  mill!? 


SINGLE  RULE  OF  THREE  DIRECT.  67 

43.  How  much  will    a   grindstone,  32  inches    diameter, 
mid  u  inchos  thick,  come  to  at  5*.  per  cubic  foot? 
Sc(  Kcauition — >  32     the  diameter. 


cubic  measure.     S  16=haif  the  diameter, 

48     ' 
IG 

288 
48 


6 

inch.  s.  s.  d.  "    ' 

If  1728     :     5     ::     4608  :   13  4     Ans.   i:^s.  4d. 

44.  What  will  a  grindstone,  28  inches  diameter,    and  Sc- 
inches thick,  come  to,  at  1  dolls  90  cts.  per  cubic  foot  ? 

Ans.  2  dolls.  26  cts.  2  ms. 

45.  When  a  man's  yearly  income  is  9  19  dolls,  how  much 
8  it  per  day?  Ans.  2  doils.  6U  cts. 

46.  At  4^  percent,  what  is  the  commission  on  1525  doiis? 

Ans.  08  doll?.  62  cts.  5  ms. 

47.  What  is  the  interest  of  456  dolls,  for  1  year,  at  6  per 
lent  ?  Ans.  27  dolls.  36  cts. 

48.  At  5  dolls.  50  cts.  per  M.  what  will    21,186  feet   of 
boards  come  to  ?  Ans.  1 16  dolls  52  cts.  3  ms. 

49.  When  boards  are   sold  at  18  dolls,  per  M.   \vh;^t  is  it 
per  foot?  Ans.  I  cent  8  mills. 

50.  What  will  98  feet  of  boards  come  to  at  4  cts.  p-sr  foot? 

Ans.  3  dolls.  9  J  cts. 

51 .  What  will  49  thotisand  3  hundred  and  ^5  casts  O]  staves 
come  to  at  17  dolls,  per  tliousand  ? 

No  J  F..  Staves  are  counted  by  casting  3  at  a  time  :  40  casts 
make  I  hundred,  and  10  hundred  1  thousand. 


M. 

dolls. 

jM    h. 

c. 

If  1      : 

17     : 

:     49     3 

25 

10 

10 

493 

iO 

40 

40 

dlh.  cts.  ms. 

Casts     400  .  19715  Ans.   839    I'j  2 

52.  Wh.u  will  1 0  M.  8  and  1 5  casts  of  white-onk  hhd.  staves 
come  to,  at  31  doiis.  per  M.  ?     Ans.  6J4  dolls.  96  cts.  2  ms. 


58  SINGLE  RULE  OF  THREE  DIRECT. 

53.  What  will  22  M.  9  and  37  casts  of  red-oak  hhd.  staves 
come  to  at  13  dolls,  per  M.  ?     Ans.  298  dolls.  90  cts.  2  ms. 

54.  What  will  56  bundles  of  hoops  come  to  at  25  dolls, 
per  M.  of  30  bundles  ? 

Note.  Hoops  are  sometimes  bound  in  bundles  of  30 
hoops  each,  and  four  such  bundles  are  1  hundred,  and  ten 
hundred,  or  40  bundles,  1  thousand.  But  they  are  generally 
bound  in  bundles  of  40  each,  3  bundles  making  1  hundred, 
and  iea  hundred,  or  thirty  bundles,  1  thousand. 

3)56 

hund.     dolls.     Or  bund.  dlls.  bund. 

If     10     :     25     :  :    18|  hundreds  30  :  2h  :  :   56 

25  23 


90  280 

36  112 

I6| 


li0)46|6| 


310)U0|0 

46,66| 
46,6| 
Ans.  46  dolls.  6|  dimes,  or  66|  cts. 

55.  How  many  bushels  of  salt,  at  4  dolls.  75  cts.  per  hhd. 
can  I  have  for  326  dollars? 
dlls.cts    bush,    dolls. 
If  4  75  :  8  : :  326         Ans.  549  bushels,  when  measured 

on  board  the  vessel. 
If  4  75  :  71  :  :  326       Ans.     514    bushels    three    pecks, 
nearly,  when  measured  ashore. 
5^>.  What  is  the  tax  on  lands,  &c.  valued  at  2957  dollars 
in  the  direct  tax,  at  28  cents  and  three  mills  on  the  100  dol- 
lars ?  Ans.  8  dolls  3iS  cents  8  mills. 

57.   What  is  the  tax  on  a  house,  valued  at  900  dollars,  in 
the  direct  tax,  at  j\  per  cent  ? 

dolls.       dolls.         dolls. 
If     100     :      ,3     :  :     900 

2^ 

100)^^70,0 

Ans.  2  dolls.  70  cts. 
Or,  as  j\  per  cent,  is  equal  to  3  mills  on  the  dollar,  mul- 
tiplying the  sum  in  dollars  by  3,  gives  the  answer  m  mills. 


SINGLE  RULE  OF  THREE  DIRECT.  59 

58.  What  is  the  tax  on  753  dollars  at  j\  per  cent.? 

753  dollars 
3  mills 
2"259  Ans.  2  dolls.  25  cts.  9  ms. 

59.  Find  the  tax  on  the  following  sums,  viz. 

1 550  dolls,  at  y*^  per  cent. 
4580  j\  ... 

7850  j%  ... 

12680  j\  ... 

16950  j\  ... 

240^20  j\  ... 

35840  1  ... 

60.  What  will  a  piece  of  land,  measuring  48  feet  in  length 
and  40  in  width  at  each  end,  amount  to  at  20  dollars  per 
square  rod?  feet. 

48 
40 

feet.  dolls.       

If  272i     :     20  ::   1920 

By  decimals.  Ans.  141  dolls.  4  cts. 

If  272,25  :  20  ::    1920 

61.  A  charter-party  for  a  vessel  of  186  tons  commenced 
on  the  28th  of  May,  and  ended  on  the  tenth  of  October  fol- 
lowing :  What  does  the  hire  amount  to  for  that  time,  at  S 
dolls,  per  ton  per  month  of  30  days  ? 


dlls.cts. 

Ans 

6 

20 

- 

22 

80 

47 

10 

- 

88 

76 

135 

60 

221 

58 

358 

40 

days. 

186 

tons 

May 

4 

2 

dolls. 

per 

month. 

June 

30 

days. 

July      - 

31 

30  :  372 

August 

31 

136 

September     - 
October    - 

30 
10 

2232 

1116 

136 

372 

3,0)5059,2 

1686,40  Ans.   1686  doll?.  40  cts. 

In  calculating  the  time,  the  days  of  receiving  and  discharg- 
ing the  vessel  are  both  included. 


S9  INVERSE   PROPORTION. 


INVERSE  PROPORTION. 

Whereas  in  the  Rule  of  Three  Direct,  more  requires 
more  and  less  requires  less,  in  this  rule  more  requires  less 
and  less  requires  more. 

Rule.  Alter  stnting  the'terms  as  in  the  Rule  of  Three  Di- 
rect, mulfiply  the  tirst  arid  second  terins  together,  and  divide 
the  product  by  the  third,  and  the  quotient  is  the  answer. 

EXAMPIES. 

1.  If  ?00  workmen  complete  a  piece  of  work  in  12  davs, 
how  many  are  sufficient  to  do  it  in  three  days  ? 
d.  m.  d. 

12     :      100     ::     3 
12 


3)1200 

400  Ans.  400  men. 

2.  If  8  boarders  drink  a  barrel  of  cider  in  12  days,  how 
long  wouhi  it  last  if  4  more  came  among  them?  Ans.  t)  days. 

3.  A  ship's  comp:inv  of  15  persons  is  supposed  to  have 
bread  to  last  their  voyage,  allowing  each  8  ounces  per  day; 
when  they  pick  up  a  crew  of  5  persons  in  distress,  to  whom 
thoy  rjre  wdimg  to  communicate:  what  will  the  daily  allow- 
ance of  each  person  then  be?  Ans.  6  ounces. 

4.  When  wheal  is  sold  at  93  cents  per  bushel,  the  penny 
loaf  weighs  12  ounce?  ;  what  must  it  weigh  when  the  wheat 
is  I  dollar  24  cts.  per  bushel?  Ans.  9  ounces. 

5.  How  many  yards  of  baize,  3  qrs.  wide,  will  line  a  cloak 
which  has  in  it  12  yards  of  camblet,  half  yard  wide  ? 

Ans.  8  yards. 

6.  Suppose  400  men  in  a  garrison  are  provided  with  pro- 
visions for  thirty  days  ;  how  many  men  must  be  sent  out,  if 
they  would  have  the  provisions  last  50  days  ? 

Ans.  160  men. 

7.  What  sum  should  be  put  to  interest  to  gain  as  much  in 
1  month,  as  127  dollars  would  gain  in  12  months? 

Ans.  1 524  dolls. 


COMPOUND  PROPORTION.  61 

COMPOUND  PROPORTION 

Teaches  to  resolve  such  questions,  as  require  two  or  more 
statings  by  simple  proportion. 

Rule.  State  the  question,  by  placing  the  three  condi* 
tional  terms  in  this  order  :  that  which  is  the  principal  cause 
of  gam,  loss,  or  action,  possesses  the  first  place ;  that  which 
denotes  space  of  time,  or  distance  of  place,  the  second  ;  and 
that  which  is  the  gain,  loss,  or  action,  the  third  :  then  place 
the  other  two  terms,  which  move  the  question,  under  those 
of  the  same  name,  and  if  the  blank  place  fall  under  the  third, 
multiply  the  three  last  terms  for  a  dividend,  and  the  two 
fir^t  for  a  divisor  ;  but  if  the  blank  fall  under  the  first  or  se- 
cond place,  multiply  the  first,  second  and  last  terms  together 
for  a  dividend,  and  the  other  two  for  a  divisor;  and  the 
quotient  will  be  the  answer. 


EXAMPLES. 

1.  If  £100  in  12  months  gain  £5,  how  much  will  £400 
gain  m  3  months  ? 

£.         mo.       £. 
100     :     12  :  :  5 
400     :       3 
3 

100     1200 
12           5 

12|00)60jOO 

£5  Ans.  £5 

2.  If  8  men  make  24  rods  of  wall  in  6  days,  how  many 
men  will  build  1 8  rods  in  3  days  ? 
m.        d.         r. 
8     :     6  :  :  24 
3        18 
6 

M       108 
3  8 

72  )  864(12    .  , 

72  '^■ 

144 
^  H4  Ans.  I  2  men. 


62  COMPOUND  PROPORTION. 

3.  If  a  family  of  9  persons  spend  450  dollars  in  5  months, 
how  much  would  be  sufficient  to  maintain  them  8  months,  if 
five  more  were  added  to  the  family  ?         Ans.   1120  dolls. 

4.  What  is  the  interest  of  £240  for  50  days,  at  5  per 
cent,  per  annum  ? 

£.         days.       £. 

100  :     365  :  :  5 

240  :       50 

50 


100     12000 
365  5 


365100  )600|00(1    12  10^ 
365 

235 
20 

365)4700(12 
4380 

320 
12 


365)3840(10 
365 

190 
4 

365)760(2 
730 

30  Ans.  £1    12  10|- 

N.  B.  By  omitting  to  multiply  by  the  rate  per  cent,  and 
dividing  36500  by  it,  are  found  the  fixed  divisors  of  7300 
for  5,  and  6083  for  6  per  cent,  per  annum,  sometimes  used 
in  calculating  interest. 


COMPOUND  PROPORTION.  63 

b.  What  is  the  interest  of  654  dollars  for  1G4  days,    at  6 
per  cent,  per  annum  ? 

100  654  dollars. 

365  164 


6)36500  2G16 

6083  the  fixed  divisor,  3924 

found  as  above  directed.  6^4 


6083)107256(17,632 
6083 
46426 
42581 


38450 
36498 
19520 
18249 


12710 
12166 
544 
Ans.  17  dolls.  63  cts.  2  ms. 

6.  What  is  the  interest  of  947  dollars,  for  294  days,  at  5 
per  cent,  per  annum  ? 

947  dolls. 
294 
3788 
8523 
1894 
Fixed  divisor  7300)278418(38,139 
21900 
59418 
58400 
10180 
7300 
28800 
21900 


69000 
65700 


3300      Ans.  38  dolls.  13  cts.  9  ms. 


64  VULGAR  FRACTIONS. 

VULGAR  FRACTIONS. 

Fractions,  or  broken  numbers,  are  expressions  for  anj 
assignable  parts  of  an  unit;  and  are  represented  by  two 
numbers,  placed  one  above  the  other,  with  a  line  drawn 
between  them. 

The  number  above  the  line  is  called  the  numerator^  and 
that  below  the  line  the  denominator. 

The  denommator  shows  how  many  parts  the  integer  is 
divided  into,  and  the  numerator  shows  how  many  of  those 
parts  are  meant  by  the  fraction. 

Fractions  are  either  proper,  improper,  compound,  or 
mixed. 

1st.  A  proper  fraction  is  when  the  numerator  is  less  than 
fhe  denominator,  as  ^,  §,  ^\,  f|,  &,c. 

2d.  An  improper  fraction  is  when  the  numerator  is  either 
equal  to  or  greater  than  the  denominator,  as  |,  y ,  jf,  |f ,  &c. 

3d.  A  compound  fraction  is  a  fraction  of  tractions,  and 
known  by  the  word  of  as  a  of  f,  f  of /^,  ||  of  |J,  &c. 

4lh.  A  mixed  number  or  fraction  is  composed  of  a  whole 
number  and  a  fraction,  as  8f ,  17^,  293,  &c. 

I.  To  redute  a  simple  fraction  to  its  lowest  terms. 
Rule.  Find  a  common  measure  by  dividing  the  lower 
term  by  the  upper,  and  that  divisor  by  the  remainder,  con- 
tinuing till  nothing  remains ;  the  last  divisor  is  the  common 
measure ;  then  divide  both  parts  of  the  fraction  by  the  com- 
mon measure  ;  the  quotients  express  the  fraction  required. 

Note.  If  the  common  measure  happens  to  be  I,  the  frac- 
tion is  already  in  its  lowest  term ;  and  when  a  fraction  hath 
ciphers  at  the  right  hand,  it  may  be  abbreviated  by  cutting 
ihem  off,  as  m. 

EXAMPLE. 

}.  Deduce  jYt  ^^  ^^^  lowest  term. 
91)117(1 
91 

26)91(3 

78 

(Common  measure     13)26(2 

26  i''^)h\{i  *^^^  answer. 


VULGAR  FRACTIONS.  65 

Or,  divide  the  terms  of  the  fraction  by  any  number  that 
will  divide  them  without  a  remainder;  divide  the  quotients 
in  the  same  manner,  and  so  on,  till  no  number  will  divide 
them  both,  and  the  last  quotients  express  the  fraction  in  its 
lowest  terms. 

EXAMPLES. 

2.  Reduce  j-Sf  to  its  lowest  terms. 

(8)     (8)     (3) 
192     24       3     1 

= — = — =-  the  answer. 

576     72       9     3 

3.  Reduce  l^  to  its  lowest  terms.  -  Ans.     | 

4.  Reduce  |^f  to  its  lowest  terms.     -         -        Ans.     f 

5.  Reduce  ||^J-  to  its  lowest  terms.         -  Ans.  |i 

II.  To  reduce  a  mixed  number  to  an  improper  fractian. 
Rule.  Multiply  the  whole  numbers  by  the  denominator  of 

the  fraction,  and  to  the  product  add  the  numerator  for  a  new 
numerator,  and  place  it  over  the  denominator. 

Note.  To  express  a  whole  number  fraction-wise,  set  one 
for  a  denominator  to  the  given  number. 

examples. 

1.  Reduce  5f  to  an  improper  fraction. 

5x8-f  3=V  the  answer. 

2.  Reduce  ISS/y  to  an  improper  fraction.  Ans.  3|i8 

3.  Reduce  27^  to  an  improper  fraction.  Ans.     2^5 

4.  Reduce  514/g  to  an  improper  fraction.  Ans,   82,|y 

III.  To  reduce  an  improper  fraction  to  its  proper  terms. 
RuLF.  Divide  the  upper  term  by  the  lower,  and  the  quo- 
tient will  be  the  whole  number;  the  remainder,  if  any,  will 
be  the  numerator  to  the  fractional  part. 


1.  Reduce  y  to  its  proper  terms. 

5)17(3|  the  answer. 
15 

2 

2.  Reduce  215  to  its  proper  terms.  Ans.  27f 

3.  Reduce  «ff  ^  to  its  proper  terms.  Ans.  biij\ 

G2 


66  VULGAR  FRACTIONS. 

IV,      To  find  the  least  common  multiple  07'  denominator. 

Rule.  Divide  the  given  denominators  by  any  number  that 
will  divide  two  or  more  of  them,  without  a  remainder,  and 
set  the  quotients  and  the  undivided  numbers  underneath. 
Divide  these  quotients  and  undivided  numbers  by  any  numr 
ber  that  will  divide  two  or  more  of  them  as  before,  and  thus 
continue,  till  no  two  numbers  are  left  capable  of  being  less- 
ened. 

Multiply  the  last  quotient  and  the  divisor  or  divisors  to- 
gether, and  the  product  will  be  the  least  common  denomina- 
tor required. 

EXAMPLES. 

L  What  is  the  least  common  measure  off,  f,  /-,  and  f^g  ? 
8)9     8     15     16 


3)9     1      15 


3     15       2 

3X5X2=30X3X8=720,  Ans. 
fi.  What  is  the  least  number  that  can  be  divided  by  the 
aine  digits  without  a  remainder  ?  Ans.  2520. 

V.      To  reduce  vulgar  fractions  to  a  common  denominator. 

Rule.  Find  a  common  denominator  by  the  last  case,  in 
which  divide  each  particular  denominator,  and  multiply  the 
quotient  by  its  own  numerator  for  a  new  numerator,  and  the 
new  numerators,  being  placed  over  the  common  denomina- 
tor, express  the  fractions  required  in  their  lowest  terms. 

examples. 

1.  Reduce  J,  f  and  y^  to  a  common  denominator. 
36  the  common  denominator. 

4  9X3=27 

9  4X5=20 

12  3X7=21 

The  fractions  will  be  |J,  |f ,  |i. 
%  Reduce  f ,  |,  |  and  J  to  a  common  denominator. 

Ans.  If,  if,  iJ,  andfi. 
3.  Reduce  |,  f ,  f  and  /j-  to  a  common  denominator. 

Ans.  ||,f|,HandJ.|. 
Af  Reduce  J')  I,  x*j  aud  f  to  a  common  denominator. 

Ans.  ih  Ih  if  and  f  f . 


VULGAR  FRACTIONS.  67 

VI.     To  reduce  a  compound  fraction  to  a  single  one. 
RuLpfl  Multiply  aU  the  numerators  for  a  new  numerator, 
and  all  the  denominators  for  a  new  denominator,  then  reduce 
the  new  fraction  to  its  lowest  term  by  Case  I. 

EXAMPLES. 

1.  Reduce  f  of  f  of  ^^  to  a  single  fraction. 

3X5X   9=135     9, 

= — the  answer. 

4X6X10=240     16 

2.  Reduce  f  of  ^  of  |^  to  a  single  fraction.       Ans.  //^ 

3.  Reduce  f  of  f  of  f  to  a  single  fraction.  Ans.  /j 

VII.  To  reduce  a  fraction  of  one  denomination  to  the  fraction 

of  another^  but  greater^  retaining  the  same  value. 

Rule.  Reduce  the  given  fraction  to  a  compoimd  one,  hy 
multiplying  it  with  all  the  denominations  between  it  and  that 
denomination  to  which  you  would  reduce  it ;  then  reduce 
that  compound  fraction  to  a  single  one. 

EXAMPLES. 

^     1.  Reduce  ^  of  a.  penny  to  the  fraction  of  a  pound. 
d 
7X1X1  7 

= the  answer. 

8X12X20   1920 

2.  Reduce  a  of  a  pennyweight  to  the  fraction  of  a  pound 
Troy.  Ans.  ^^^ 

3.  Reduce  ^  of  a  pound  Avoirdupois  to  the  fraction  of  a 
cwt.  Ans.  j}^ 

VIII.  To  reduce  the  fraction  of  one  denomination  to  the  frac- 
tion of  another.^  hut  less^  retaining  the  same  value. 

Rule.  Multiply  the  numerator  by  the  parts  contained  in 
the  several  denominations  between  it  and  that  denomination 
to  which  you  would  reduce  it  for  a  new  numerator,  and 
place  it  over  the  denominator  of  the  given  fraction. 

EXAMPLES. 

1 .  Reduce  ^^^  of  a  pound  to  the  fraction  of  a  peany. 
1X20X12=240 

— =1  the  answer. 
960 


68  VULGAR  FRACTIONS. 

2.  Reduce  3^^^  of  a  lb.  Troy  to  the  fraction  of  a  dwt. 

Ans.  f 

3.  Reduce  yig;  of  a  cwt.  to  the  fraction  of  alb.     Ans.  ^ 

IX.      To  find  the  value  of  the  fraction  in  the  known  parts  of  the 
integer. 

Rule.  Multiply  the  numerator  by  the  known  parts  of  the 
integer,  and  divide  by  the  denominator. 

EXAMPLES. 

L  AVhat  is  the  value  of  |  of  a  lb.  ? 
2 
20  shillings. 


3)40 


Ans.   13^.  4^^. 

2.  What  is  the  value  of  |  of  a  shilling?     Ans.  4d.  3|  qrs. 

3.  Reduce  |  of  a  lb.  Troy  to  its  proper  quantity. 

Ans.  7  oz-  4  dvvt. 

4.  Reduce  |  of  a  mile  to  its  proper  quantity. 

Ans.  6  fur.  16  poles, 

X.      To  reduce  any  given  quantity  to  the  fraction  of  a  greater 
denomination  of  the  same  kind. 

Rule.  Reduce  the  given  quantity  to  the  lowest  denomina- 
tion mentioned  for  a  new  numerator,  under  which  set  the 
intregal  part  (reduced  to  the  same  name)  for  a  denominator, 
and  it  will  express  the  fraction  required. 


1.  Reduce  16j.  Zd.  to  the  fraction  of  a  pound. 

16     8 
1^ 

2©0     5 

=-the  answer. 

240     6 

2.  Reduce  2  quarters  3^  nails  to  the  fraction  of  an  ell  En- 
glish. Ans.  f 

3.  Reduce  4*.  6-J-ci.  to  the  fractioa  of  a  pound.    Ans.  f  Jf 


VULGAR  FRACTIONS.  6» 

ADDITION  OF  VULGAR  FRACTIONS, 

I.   To  add  fractions  that  have  a  common  denominator. 

Rule.  Add  their  numerators  together,  and  place  the  suta 
over  one  of  the  given  denominators. 

EXAMPLES. 

1.  Add  ^,  J,  f,  ^  and  |  together. 

1 
2 
4 
5 
7 

19 

-Q=2^  the  answer. 

2.  Add  /^,  |i  and  if  together.  Ans.   12^. 

3.  Add  ig^  \l  and  /^  together.  Ans.   l|^. 

4.  Add  j\,  }|  and  ||  together.  Ans.  2yV- 

II.     To  ac2<i  mixed  numbers  whose  fractions  have  a  common 
denominator. 

Rule.  Add  the  fractions  by  the  last  case,  and  the  integers 
as  in  whole  numbers. 

EXAMPLES. 

1.  Add  2j\^  3r\,  4j\  and  7y\  together. 

'TT 

17y\  answer. 

2.  Add  13yV?  9tt>  and  3/^,  together.  Ans.  25|. 

3.  Add  It>5,  2fV,  3y\  and  4ii  together.  Ans.  12. 

4.  Add  9jf ,  7yV,  5t*4  and  8H  together.  Ans.  314. 

III.   To  add  fractions^  having  different  denominators. 

Rule.  Find  the  least  common  denominator  by  Case  IV,  in 
Reduction,  in  which  divide  each  denominator,  and  multiply 


70  VULGAR  FRACTIONS. 

the  quotient  by  its  numerator ;  the  sum  of  the  products  is  a 
new  numerator  to  the  common  denominator,  and  the  fraction 
required. 


EXAMPLES. 

1.  Add  I,  1, 1,  f  and  H  together. 

24  com.  denominator. 

3  8x  2  =  16 

4  6X  3=18 
6  4X  5  =  20 
8  3X  7=21 

12     2X11=22 

|J=4^\^  the  answer. 

2.  Add  I,  i,  i,  4  and  |  together.  Ans.  l^Vj^. 

3.  Add  f ,  I,  f ,  f  and  fy  together.  Ans.  3j\\, 

IV.   To  add  mixt  numbers  whose  fractions  have  different  de- 
nominators. 

Rule.  Add  the  fractions  as  in  the  last  case,  and  the  inte- 
gers as  in  whole  numbers. 


Add  5|,  6f  and  4^  together. 

24  com.  denominator. 


5| 


Ans.  17^V 


16 
21 
12 


2.  Add  If,  ^  of  JL  and  9 i^*  together.  Ans.  11^^^. 

3.  Add  \\%'^  6|,  I  of  i  and  7^  together.        Ans.  le^Vo- 

V.    When  the  fractions  are  of  several  denominations. 

Rule.  Reduce  them  to  iheir  proper  quantities  by  Case  IX 
in  Reduction,  and  add  as  before. 


VULGAR  FRACTIONS.  71 


1.  Add  J  of  a  £  to  j\  of  a  shilling. 

15  common  measure. 
s.      d. 


J  of  a  £=15     6§ 
/^ofa5.=0     3| 


Ans.   15  10y4_ 


10 
9 


1  5  —  *  IS 

2.  x\dd  I  of  a  yard,  |  of  a  foot,  and  |  of  a  mile  together. 

Ans.   1540  yds.  2  ft.  9  inches. 

3.  Add  ^  oi  a  week,  ^  of  a  day,  and  j  of  an  hour,  together. 

Ans.  2  days  14^  hours. 


SUBTRACTION  OF  VULGAR  FRACTIONS, 

I.   To  find  the  difference  between  simple  fractions  that  have  a 
common  denominator. 

Rule.     Subtract  the  less  numerator  from  the  greater,  and 
under  the  remainder  put  the  denominator. 


EXAMPLES. 

From 
Take 

4 

13 

If 

m 

Rem. 

? 

\ 

3 

4 

5V 

jfir 

II.   To  subtract  a  fraction  or  mixt  number  from  a  whole  number. 

Rule.  Subtract  the  numerator  from  the  denominator,  and 
under  the  remainder  put  the  denominator,  and  carry  one  to 
be  deducted  from  the  integer. 


EXAMPLES. 

From 

3 

G 

10 

9 

100 

Take 

Oy'e 

Of 

OtV 

H 

9Wir 

Rem. 

m 

^ 

9tV 

Sf 

OriT 

72  VULGAR  FRACTIONS. 

III.  To  subtract  simple  fractions  that  have  no  common  deno 
minator. 
Rule.  By  case  IV  in  Reduction,  find  a  common  denomi 
nator,  in  which  divide  each  denominator,  and  multiply  the 
quotient  by  its  numerator;  the  difference  between  the  pro- 
ducts thus  found  is  a  numerator  to  the  common  denominator, 
and  the  answer  required. 

Iexamples. 
From  ^^  take  ^-^ 

42  com  denom. 

21     2x17—34 
14     3x    9=27 


Rem   4\=^  the  answer. 

From    f  ff  I  ^%  ^^ 

Take  ^  f^  £  ^  ^ 

In  order  to  distinfifuish  the  greater  of  two  fractions,  let 
them  be  reduced  to  -a  conjmon  denominator,  as  in  case  V  in 
Reduction  ;  and  that  fraction,  whose  numerator  is  greater, 
is  the  er^ater  fraction  ;  the  difierence  between  the  new 
numerators,  being  set  over  the  common  denominator,  will 
shew  the  excess  or  inequality. 


Which  of  the  two  is  the  greater  fraclion,  \l  or  }|  ? 
48  com  denom. 


12     4X11=44 

16     3X15=45      Ans.  if  is  greater  by  Jj^. 

IV.      To  subtract  a  fraclion  or  mixt  number  from  a  mixt  num- 
ber^ when  the  fractional  part  to  be  subtracted  is  greater  than 
that  from  which  it  is  to  be  subtracted. 
Rule.  Find  a  common  denominator  and  a  new  numerator, 
as  in  the  last  case,  and  then  subtract  the  numerator  of  the 
greater  fraction  from  the  common  denominator,  and  to  the 


VULGAR  FRACTIONS.  73 

remainder  add  the  less  numerator,  and  set  the  sum  of  hoth 
for  a  new  numerator  over  tlie  common  denommator,  and 
carrv  one  to  the  integral  part,  and  proceed  as  in  whole  num- 
bers. 


EXAMPLES. 

27  common 

deuominalor. 

From 

^H 

r'Xl   =  3 

Take 

m 
4H 

1X14=14 

1  6 

5T 

From  6f 

10,-^ 

»2/5 

19fV 

Take  Of 

h\ 

H 

Vk 

Rem.  5f 

m 

Hi 

ma 

V.    When  the  fractions  are  of  d'iff:'rent  denominations. 

Rule,      Reduce  them  to  their  proper  quantities,    and  suh- 
iract  as  before. 

rxAMPLrs. 

].  From  5  of  a  ;£  take  -^^^  of  a  sluliinpf. 

15  common  denominator. 


S. 

d 

— 

jr 

of  a 

£- 

15 

62- 

10 

1  y 

of  a 

5.= 

0 

^ 

9 

Rem.   15     3^'. 

2.  From  J  of  a  £  take  ^-  of  a  shillinsr.         Ans.   14^   3J. 

3.  From  £  of  a  lb.  troy  tako  ^  of  ;ui  ounce. 

Ans    8  oz.  16  dwt.  IG  f^rs. 

4.  From  7  weeks  take  9/^  days.    Ans.  5w.  4d.  7h.  l^m. 

5.  From  J- of  a  yard  take  2.  of  an  inch.     Ans.  5  inch.  1  be. 


MULTIPLICJITIOJV  OF  FULGJIR  FRACTIOXS. 

Rule.  Reduce  compound  fractions  to  simple  onrs,  and 
mixt  nuTihers  to  irn;)ro()er  fractions;  <h:'n  muU"p!v  t!i?  nu- 
m  r,t<or3  to?2;et!ior  for  a  new  numerator,  and  the  denomina- 
tors for  a  n*?.v:  denominator. 

II 


4 

VULGAR  FRACTIONS. 

EXAMPLES. 

1. 

Multiply  4i  by  f 

2 

9X1 

=:fj  the  answer. 

2X8 

2. 

Multiply  f  by  ^ 

Ans. 

A 

3. 

Multiply  i  by  | 

Ans. 

i4 

4. 

Multiply  48f  by  13f 

Ans. 

072^ 

5. 

Multiply  1  or  9  by  1 

Ans. 

^11 

6. 

Multiply/^  by  1  off  off 

Ans. 

3 

8 

DIVISION  OF  VULGAR  FRACTIONS, 

Rule.     Prepare   the  fractions  if  necessary ;     then  invert 
the  divisor,  and  proceed  as  in  multiplication. 


EXAMPLES. 

1. 

Divide 

4i>y| 

4X3 

■  lE  —  o 
1  4 — 7 

the 

answer. 

7X2 

o 

Divide 
6 

31  by  9 
2 

h 

19X   2 
y>         y     Then  —     —  TV4=i  ^^^  answer. 
6X19 

3.  Divide  5  by  y*^^  Ans.  7^ 

4.  Divide  ^%  by  4^  Ans.  ^- 

5.  Divide  9^  by  i  of  7  Ans.  ^2^^ 

6.  Divide  52051  by  |-  of  91  Ans.  7U 

mSCELLANEOUS  QUESTIONS 

m    TUK    rRECET'IKG    BULES. 

1.  What  part  is  28j|  of  33^V  •  Ans.  | 

2».  What  will  remain  if  I3^s.  and  I'^d.  be  taken  from  £1? 

An?.  b$.  6# 


VULGAR  FRACTIONS,  75 

3".  Which  is  the  greater  fraction,  j\  or  -^^  ? 

Ans.  y8_  i§  greater  by  j\ 
*       4.  Ot  what  number  is  176  the  \^  part?  Ans.  368 

5.  By  how  Tiuch  mast  you  multiply  I3|  that  the  product 
may  be  49^  ?  Ans.  3f 

6  Find  two  numbers  so  that  f  J  of  the  one  will  be  as  much 
as  j\  of  the  other  ?         Ans.   126  &  208,  or  63  Sl  104,  &c. 

7.  Which  is  greater,  }  of  6*.  or  l^.  2Jc^.  ? 

Ans.   1*.  2ic^.  is  greater  by  j\d, 

8.  A  has  I  of  I  of  a  ship,  and  B  f  of  |,  which  is  the  great- 
est share,  and  by  how  much  ?  .   Ans.  A's  share  is  greater  byj 

9.  \  farmer,  being  asked  how  many  sheep  he  had.  an- 
swere  1,  that  he  had  them  in  5  fields;  in  the  first  he  had  i 
ot  his  tlock,  in  the  second  },  in  the  third  |,  in  the  fourth  J^, 
and  in  the  fifth  450  ;  how  many  had  he  ?  Ans.   1200. 

RULE  OF  THREE  DIRECT  IJV  VULGAR  FRACTIOA'S, 

Rule.  Having  stated  the  question,  make  the  necessary 
preparations,  as  in  Reduction  of  Fractions,  and  invert  the 
lirst  term  }  then  proceed  as  in  Multiplication  of  Fractions. 

EXAMPLES. 

1.  If  1  of  a  yard  of  cloth  cost  |  of  a  shilling,  what  will  f 
of  a  yard  come  to? 

yd.  s.  yd, 

Ifx  :  ^  ::  1 

inverted. 

4X2X7     s. 

=11=2^.  4d.  the  answer. 

lX3i^8 

2.  If  j\  of  a  ship  cost  £273  2*.  6d.  what  are  /^  of  her 
worth?  Ans.  £227   12^    Id. 

3.  If  I  of  a  yard  cost  |  of  a  pound,  what  will  f  of  an  ell 
English  come  to,  at  the  same  rate  ?  Ans.  £2. 

4.  \  person,  having  |  of  a  coal  mine,  sells  f  of  his  share 
for  £i71  ;  what  is  the  whole  mine  valued  at? 

Ans.  £380: 


PRACTICE. 


SIJVGLE  RULE 


OF  THREE  LYVERSE 
FRACTIONS. 


LY  VULGAR 


EXAMrm:s. 

1.  If  25f5.  will  pay  for  the  carriage  of  an  cwt.  145}  miles, 
how  far  mi\y  6i  cwt.  be  carried  for  the  same  money? 

Ads.  22/^  miles. 

2.  If  3:{- 3'(ls.  ofcloth  that  is  I^  yard  wide  be  sufficient  to 
make  a  cioak,  how  much  must  I  have  of  that  sort  which  is 
I  yard  wide,  to  make  another  of  the  same  bigness  ?  Ans.  4  J  y. 

3.  If  3  men  can  do  a  piece  of  work  in  4^  hou^s,  in  how 
many  hours  will  10  men  do  the  same  work?         Ans.   1/^ 

4.  {f  the  penny  white  loaf  weigh  7  oz.  when  a  bushel  of 
wheat  costs  5*.  6d.  what  is  the  bushel  worth  when  the  penny 
while  loaf  weighs  but  2^  oz.?  Ans.  15^.  4|c?. 


PRACTICE 

Is  a  contraction  of  the  Rule  of  Three  Direct,  when  the 
first  term  happens  to  be  an  unit  or  one,  and  has  its  name 
from  its  frequent  use  in  business. 

THE  TABLE. 


P^artsofa£. 

Parts  of  a  Ton. 

Parts  ofi  Cwt. 

s.     d. 

cwt.    qr. 

ii. 

10         is        ^ 

10           is  i 

28       is           -J- 

6     8  -         1 

5           -     i 

14       -             i 

5         -         1 

^          -    i 

8       -             4- 

4         .         1 

Q       O       .       1 

7       -             ^- 

3     4  -         i 

2 

4       - 

2     6-         I 
2         -          > 

1 

3^^    -           tV 
2       -            -'- 

^^ 

Parts  of  a  Cwt. 
(jrs.    lb. 

1     8  -        -V 
1          -        -J 

Parts  of  a  J-  Cwt. 

/                                   2  0 

Parts  of  a  Shilling. 

2           is  i 
1                i 

lb. 

U       is           1 

0  is   Jt. 
4     -     I 
3     .     1 

2     -     i 

1  -   r'. 

7       -             1 
4       -             1 

8      -X 

7      tV 
4      h 
2      .V 

3^     -            i 
2       -            tV 

1      -         ^V 

PRACTICE. 


77 


Case  I. 
When  the  price  is  an  aliquot  or  even  part  of  a  shilling. 

Rule.  Divide  the  given  number  by  the  part,  and  the 
quotient  is  the  answer  in  shillings ;  what  remains  is  to  be  re- 
duced as  in  Compound  Division. 

EXAMPLES. 

1.  What  will  4596  yards  cost  at  6c?.  per  yard  ? 


6(/. 

i 

4596 

2|0 

22918 

114      18 

2. 

yds, 
3746 

at 

d. 

4  per  yard. 

3. 

1095 

3 

4. 

7596 

2 

5. 

3747 

1 

6. 

3203 

H 

- 

Ans. 

£114   ISs, 

£ 

s. 

d. 

Ans 

.62 

8 

8 

- 

13 

13 

9 

- 

63 

.6 

0 

- 

15 

12 

3 

- 

20 

0 

n 

Case  II. 

When  the  price  is  pence^  or  pence  and  farthings^  and  no  even 

part  of  a  shilling. 

Rule.     Find  the  even  parts  for  the  price,  and  proceed  as 
in  Case  I,  and  the  sum  of  the  quotients  is  the  answer. 


EXAMPLES. 

1.  What  will  4937  yards  come  to  at  9d.  per  yard? 

4937 


210 


2168  6 
1234  3 

370|2  9 


Ans.  £185  2  9 
H2 


8 

PRACTICE. 

yds. 

d 

£ 

s. 

il 

2.   2765  at 

8  pe 

r  yard, 

Ans.  92 

3 

4 

3.  3762 

7 

- 

-  109 

14 

6 

4.  3159 

^i 

- 

.   98 

14 

H 

5.  1496 

11 

- 

-   G8 

11 

4 

6.  1895 

»0i 

- 

-   82 

18 

H 

7,  46891 

5 

- 

-   97 

13 

Hi 

8.  3689 

H 

- 

-  126 

16 

2i 

9.  1871 

H 

- 

-   19 

9 

n 

10  8914 

H 

- 

-  306 

8 

H 

11.  25631 

9i 

- 

-  101 

9 

5; 

12.   95| 

m 

- 

4 

3 

H 

13.  201J- 

9 

- 

7 

10 

iH 

Case  III. 

When  the  price  is  shillings^  or  shillings  and  pence^  and  an  even 
part  of  a  pound. 

Rule.  Divide  the  given  quantity  by  the  even  part,  and 
the  quotient  is  the  answer  in  pounds.  If  there  be  a  remain- 
der, reduce  it  as  in  Compound  Division. 

EXAMPLES. 

1.  At  6s.  Bd.  per  yard,  what  will  473  yards  come  to? 
Qs.  Sd.  I  i-  I  473 


yds. 

s.  d. 

2. 

387  at 

10 

3. 

478 

5 

4. 

397 

3  4 

5. 

797^ 

2  6 

6. 

1591- 

1  8 

Ans.  £157   13.^.  4d. 
-        -         -        Ans. 


£ 

s.   d. 

193 

10  0 

119 

10  0 

66 

3  4 

99 

13  9 

13 

5  5 

Case  IV. 

When  the  price  is  shillings.,  or  shillings  and  pence^  which  make 

no  even  part  of  a  pound. 

Rule.     Find  the  even  parts  for  the  price,  and  divide  as  in 

Oase  HI,  or  multiply  the  given  quantity  by  the  shillings,  and 

tilie  the  even  parts  of  shillings  for  the  pence,  as  in  Case  If. 


PRACTICE. 


79 


EXAMPLES. 

[.  What  co<;t  ?87  yards    at  17*.  6cl  per  yard? 

First  method.  Second  methoU. 

287  287 

17  6 


s.   d. 

10    i  h 

143  10 

5     k 

71  16 

2  6       k 

35  17  6 

Ans. 

251/.  2s.  6d 

yards. 


s.     d. 


2. 

8i72   at 

15 

3. 

3691 

19 

4. 

4765 

11 

8 

6. 

3718 

18 

4 

6. 

709i 

12 

6 

7. 

2i3 

14 

10 

8. 

96i 

2 

H 

9. 

158 

6 

81 

10. 

47051 

3 

9  , 

11. 

127 

7 

51 

2009 

287 

6  1  i  1  143 

6 

210)5022 

Ans.  251 

I.  2s.  ed. 

£.     s. 

d. 

Ans. 

6129 
3506  9 

2779  11 

B 

3408  3 

4 

443  6 

7i 

157  ;9 

6 

13  9 

4| 

45  5 

2i 

882  6 

61 

47     9  lOi 

Case  V, 

Whe?i  the  price  is  an  even  number  of  shillings. 
Rule.     Multiply  the  quantity  by  half  the  shillings,  dou- 
bling the  first  (or  right  hand)  figure  of  the  product  for  shil- 
lings )  the  rest  are  pounds. 

EXAMPLES. 

I.   What  will  788  yards  come  to  at  2^.  per  yard? 
788 

l=half  the  shillings. 


yards. 

2. 

'347 

3. 

638 

4. 

5894 

6. 

246 

6. 

3241 

7. 

523 

8. 

745 

9. 

373i 

10. 

270 

1. 

1724 

2t 

S94 

at 


Ans.  £78   16 

s.  £      i: 

4  -        •        -        -         .         ^      Ans.     69     8 

6 191     B 

8 235  J  4 

10 123     0 

12 194  17 

14 S66     2 

16 -         .  696     0 

18 386     3. 

20  * 270     0 

22  -         ...  w         -  189  15 

24  -----  -  307     2 


80 


PRACTICE. 


Case  VI. 

JVhen  the  price  is  pounds^  shillings^  4*c. 

Rule.  Multiply  the  integers  of  the  given  quantity  by  the 
pounds,  and  work  ibr  the  shillings,  &c.  by  such  of  the  pre- 
ceding rules  as  you  think  best,  and  work  likewise  for  the 
fractional  parts  of  the  integer;  the  sum  of  these  will  give 
the  answer. 

EXAMPLES. 

1.  What  will  173  cwt.  1  qr.  14  lb.  of  sugar  come  to  at 
£3  155.  (yd.  per  cwt.t 

173     1    14 
3   15     6 


s.  d. 

519 

10 

J. 

86   10 

5 

± 

43     5 

6 

tV 

4     6     G 

1  qr. 

1  ■ 

4 

0  18   lOi 

14  lb. 

0     9     5^ 

Ans.  £654     9     9| 


cwt.  qrs. 
2i9     2 
310     3 


lb. 

19 

22 


at 


69 
53 


d. 
11 

8 


Ans. 


£     s.  d. 

7G7   18  61 
834     7  5^ 


In  w^orking  questions  of  this  kind,  when  the  quantity  is  not 
above  the  multiplication  table,  the  following  method  is  used. 

1.  What    will  45  cwt.    2  qrs.  14  lb.  of  sugar  come    to  at 
£3  7  9  per  cwt.? 

3     7     9 
5 


16      18     9 
9 

2  qrs.  } 
14  1b.    \ 

Ans. 

152       8     9     price  of  45  cwt 
1      13   UU    price  of  2  qrs. 
0    -  8    .hi  price  of  14  lb. 

£154   11      I 

PRACTICE. 

tonsxwi. 

qr.  lb,                 £     s.     d. 

2. 

67 

2     8-         -     3     17     9 

8. 

19 

3   13         -            2       5  10 

4. 

75 

3  25    -         -            48     5 

6. 

2 

1   18         -         -        59     8 

6. 

1 

1   11      -         -            63     9 

7. 

0 

3   19         -         -        54     0 

8. 

37  14 

2  14  hemp          89     6     8 

9. 

27   56 

3  18     -         -      SO   iO 

10. 

15 

2               -            ^2     5     - 

11. 

17  10 

2         -         -         i  I   10 

81 
£  s.    d. 

223  {6  2 
-   45  iO  6 
183  18  .44 
7  3^0 
4  5  1ii 
2  9  7| 
per  ton   3370  IS     2 
2520  0  5 

71  9  10^ 
1603  10  9 


1.  What  will  .37  cwt.  3  qrs.  7  lb.  of  sugar  come  to,  at  14 
dolls.  40  cts.  p<r  cwt.  ? 

14,40 
37 

10080 
4320 

2  qrs.    i  720 

1  qr.      i  360 

7  1b.      4  90 

544,50  Ans.  544  dolls.  50  cts. 

tons.cwt.  qrs.  lb.  dolls,  cts.  dolls,  cts. 

2.  24     i8     3     18  of  hemp  at  289  50  per  ton.  Ans.  722-    73 

3.  31      16  268  75  8546  25 

4.  j9     14     2     12  iron  110  2170  33  S 

5.  17     3     24  cordage         14         per  cwt.  251   50 
jf .     R.  per.             dolls,  cts.                                         dolls,  cts. 

6.  25       2  25  of  land  at  29        per  acre.  Ane.     744     3 

7.  87       1   37  33  2886  88 

8.  229       3  18  18  50  4252  45^ 

9.  3  26  25  22  81 


1.  How  much  will  49  M.  3  hund.  25  casts  of  staves  come 
to  at  17  dolls,  per  M. 

49 
17 

843 

49 
2  hund.       \  3,4 

1  i  1,7 

20  casts       k  ,85 

5  4  ,212 

839,162  Ans.  839  dolls.  16  cts.  2  m?; 


« 


C2  PRACTICE. 


2. 
3. 
4. 
5. 

19 

22 

28 

4 

Wha 
^5.  6(/. 

8  15  VV.O.  bhd. 

9  37   K.O.     do. 

1  8   W.O.  bbl. 

2  11 

stave 
do. 
do. 

dolls, 

s,3i  perM.    Ans. 
13 
16 
15 

chantable  boards 
ings. 

dolls. 

614 

298 

449 

63 

com( 

96 
90 
92 
41 

1. 
at  8c 

t  will  8,767  feet   ot 
per  M.? 

8,767 
38 

mer 
6 

i  i9 

70136 
26301 
6d.     j         4383 

'shill: 

20)337,529 

£ 

e.     J. 

36 

8     8 

5 

5     2« 

0 

13     4} 

0 

3     9 

tbe 

15th  of 

Ans.  £16   17  6i 
Th*^  fourth  figure  of  the  product  of  the  remainder,  multi- 
plied   by  12,  is  set  down  for  pence,   and  the  product  of  this 
last  remainder  multiplied  by  4  for  farthings. 

*.    d. 

2.  18,370  ft.  mer.  boards,  39  8  per  M.      Ans. 

3.  2,819  do.  do.       do        37  4 

4.  ,327  do.  do.       do.       41   0 

5.  ,183  do.  refuse  do.     20  6 
What  is  the  amount  of  a  seaman's  wages  from 

March   to  the  6th  of  December  following,    being  8  mombs 
xmO  20  days,  at  16  dollars  per  month  ? 
16 
8 

1 28  for  8  months. 
15  days     8 
5  2,66| 

n8,66|     Ans.  138  dolls.  66|^  cents. 

Note.     In  calculating  the  time  of  seamen's  service,  either  the  day  <jf 
.engaging  or  being  di  -charged  is  taken,  but  not  both. 

What  is  the  amount  of  a  seaman's  vsages  from  the  15th  of 
June  to  the  28th  of  May  following,  at  15  dolls,  per  month  ? 

Ans.  171  doils> 


TARE  AND  TRFT.  83 

At  £4  11  3  per  cwt.  what  vvlii  6  qrs.  25^^  lb.  come  to? 
£4   11     3 

2  qrs. 

1  qr. 

14  lb. 

7 

1 

Ans.  £4    9    ^^ 

Whit  will  19  tons,  19  cwt.  3  qr?   27 j  lbs.  come  to  at  £19 
195.  n^c/.  perton?  Ans.  "^oiiS  ly^.  b\m^ 


1 

2 

2 

f) 

n 

1 
2 

1 

2 

9J 

i 

0 

li 

H 

1 

2 

0 

5 

8/j 

1 

2 

0 

2 

J03\ 

4 

0 

CI 

y,v. 

TARE  AND  TRET 

Are  allowances  made  in  selling  goods  by  weight. 

Tare  i«  an  allowance  made  to  the  buyer  for  th^  weight  of 
the  hogshead,  barrel,  or  bag,  containing  the  commodity. 

Tret  is  an  allowance  for  waste,  dust,  ^c.  generally  at  4  lb. 
per  104  lb, 

Cloff  IS  an  allowance  for  the  turn  of  the  scale,  at  2  lb.  per 
3  cwt. 

Gross  weight  is  the  whoFe  weight  of  the  goods,  together 
with  the  hogshead,  barrel,  or  bag,  &c.  that  contains  them. 

Suttle  is  when  part  of  the  allowance  is  deducted  from  the 
groRH. 

Neat  weight  is  what  remains  after  all  allowances  are  made. 


84 


TARE  AND  TRET. 


Custom-house  allozcances  on  iea^  coffee  and  sugar. 


Tare  on  whole  chests  of  //;. 


bohea  tea     -     -     -     70 

on  every  ~  chest  do.  36 

on  quarter  do.   -   20 

on   every  chest  of 

hyson,      or     otlier 

gre'^^n      teas,      the 

gross  wt.    of  which 

is  70  ih  or  ur- wards    20 

on    every    box    of 

other  tea,   not  less 

than  oO  lb.  or  more 

than  70  lb.  gross  18 
IfSO  lb.  gross  20 

And  from  80  lb.  gross  and 

upwards      -     -     -      22 

There  is  an  allowance  of  two  per  cent,  for  leakage  on  the  quantity 
which  shall  .;ppear  to  be  cpixlained  in  aav  cafck  of  liquor  subject  to  duty 
by  -he  gallon;  and  .0  per  cent,  on  a,ll  fcer,  ale. and  porter  in  Lo.tJeg, 
and  5  per  cent,  on  all  Ovher  liquors  in  boliies  in  lieu  of  breakage;  or  the 
duties  may  be  computed  on  ihe  actual  quantity,  at  the  option  of  the  im- 
porter, to  be  made  at  the  ^jme  o/r/z/?-?/. 


Which  tare  shall  include 
rope,  canvass,  and  other 
coverings. 
Tare  for  ail  other  boxes  of 
tea,  according  to  invoice, 
or  actual  weight  thereof. 
Tare  for  colfee  in  bags  2  per 
lUO 

in  bales  3  do. 
in  casks  {^  do. 
On  sugar,  other  than  loaf- 
in  casks  12  do. 
in  boxes  15  do. 
-       -       in  bags 

or  mats  5  do. 


EXAMPLES. 

1.  Sold  ten  casks  of  alum,  weighing  gross  33  cwt.  2  qrs. 

15  lb.  tare  15  lb.  per  cask  :  what  is  the  amount  at  25s.  4«. 

per  cwt.  ?         '  / 
civf.  qr.  lb. 

gross     33  2   15  10  casks, 

tare         1    1    10  15  lb.  per  cask. 


neat       32   1      5 


112)150 


C.l    1    to  tare. 

/ns.  £37    13  G^- 

2.  At  1  doll.  25  cts.  per  lb.  what  will  3  chests  of  hyson 
tea  come  to,  wpi^4iing  <rross  9G  lb.  97  lb.  and  JOI  lb.  ;  tare 
20  lb.  per  chest?        ^  Ans.  292  do!!?.  50  cts. 


TARE  AND  TRET.  85 

3.  At  9  dolK  49  cts.  per  cwt.  what  will  3  hhds.  of  tobacco 
Come  to,  weighing  gross,  viz. 


ewt.  qrs. 

/&. 

Ih. 

No.    I.                 y      3 

25 

tare   149 

2.               10     2 

12 

IhO 

3.              Ill 

25 

153 
Ans.  265  dolls.  461  cts. 

4.  At  795.  9^^.  per  cwt.  how  much  wiJl  4  hhds.  of  madder 

come  to,  weighing  gro.vs  viz 

cwt.  qrs. 

/&. 

No.    1.               10     6 

4 

2.               112 

13 

3.               10      I 

16 

4.              14     3 

19 

tare  14  lb.  per  cwt. 

14  lb.  i  I     47      2      24  gross. 
5     3     24  tare. 


weigiiifig  '>Toc;s, 

viz. 

CtJ'f. 

qrs.  lb. 

No.  I. 

7 

\     14 

2. 

8 

2     21 

.3. 

7 

1     21 

4. 

6 

3     25 

5. 

7 

0     23 

6. 

8 

1     12 

41      3       0  neat.      Ans.  Z\^Q,  9  ^ 
B.   At    625.  per  cwt.    what  will  a  hhd.  of  susfar  come    to., 
rt^ighing  gross  7  cwt.  1   qr.;  tare  12  lb.  per  cwt.? 

Ans.    t:2()      1      4 

6.  At  21  cts.  per  lb.  what  will  6  hhds.  of  coffee  come  t©^ 

lb. 

tare  96 

98 

91 

90 

89 
100 
Ans.  904  dolls.  32  cents. 

7.  "What  wonld  the  a])Ove  coffee  amount  t(i.  all(nvin<>'  12  lb. 
percivl.  .\^  tare  on  the  gross  weight?     Ans.  9{U>  <)oiIs.  7  5  cts. 

W.  Ai  72..  6^A  per  cwt.  how  much  will  8  hhds.  of  sugar 
come  to,  weighing  gros^  each  8  cwt.  3  qrs.  7  lb.;  tare  12  lb. 
per  cut?  ^  Ans.    t'^^'^B  3  7} 

9.  \t  2.3  cpnts  j)er  lb  what  will  4  bags  of  coffee  come  to, 
weighing  gross  450  lb.  tare  2  per  cent    or  2  lb    [)er  U)0  lb.? 

Ans.    lul  dolls.  43  cts. 

10.  At  12  lolh.  50  ct<».  per  cwt.  what  will  3  barrels  of 
ItJgar  come  to,  vveig'i  nar  Tross,  viz. 

cwt.  qrs.  lb. 
V  No.  1.  2     2     10 

2.  2     I     21 

t.  2    0     15  tare  2nb.  perbftrrel. 

An8.82doll8.  47cti.  Tmi. 
I 


86  TARE  AND  TRET. 

11.  At  15  (lolls.  40  cts.  per  cwt.  what  will  4  hhds.  sugar 
come  to,  weighing  gross,  viz. 

cx&)t.  qrs.  lb. 
No.   I.  7     3      13 

2.  8     1      10 

3.  7     2      12 

4.  8     1     21   tare  12  lb.  per  cwt. 

Ans.  443  dolls.  43  cts.  7  ms». 

12.  A  has  in  his  possession  ahhd.  of  sugar,  weighing  gros» 
9  cwt  3  qis.  owned  equall}^  between  him  and  B.  It  is  re- 
quired to  know  how  much  sugar  he  should  weigh  out  to  B, 
allowing  tare  12  lb-  per  cwt?  Ans.  4  cwt    I'qr.  11 J  lb. 

13.  At  19i  cts  per  lb.  what  will  2  hhds.  of  coffee  come  to, 
weighing  gross  1 5  cwt-  3  qrs.  1 1  lb.  allowing  custom-house 
tare,  or  12  lb.  per  100? 

15     3     11 

15U0  3«=  fifteen  hundred. 
1 80:=  15x  12  for  excess  in  each  cwt. 
8  l=three  quarters. 
11 

Gross   1775  1775 

Tare     213  Tare  12  per  100 


Neat  1562  213.00 


14058 
1562 
731 


30459  cts.  An?.  301  dolls.  59  ct«. 

14.  B  buys  of  C  a  hogshead  of  coffee,  we  ghing  gross  ^ 
cwt.  2  qrs.;  tare  12  lb.  per  cwt.  what  will  it  amount  to  iA  23 
cts.  per  lb?  Ans.  218  do!ls  50  cU. 

15.  If  custom-house  tare,  or  12  lb.  per  100,  \\vre  aL  wed 
on  the  above  coffee,  what  would  it  amount  to,  oik!  ubal  clif- 
fercnce  would  it  niake  to  the  buyer? 

Ans.   It  amounts  to  215  dolls.  35  cts.  3  ms,  being  3  dolls. 
11  cts.  7  ms.  in  his  favour. 
IG.  What   is  the  gross  weight    of  a  hog^ilL•ad  of  tobacco, 
HveighiHg  neat  1 1  cwt.  1  qr ;  tare  14  lb.  per  cwt.? 

Ans.   12  cwt.  3  qrs.  12  lb. 


SINGLE  FELLOWSHlf.  87 

FELLOWSHIP 

Is  when  two  or  more  join  their  stocks,  and  trade  together, 
dividing  their  gain  or  loss,  in  proportion  to  each  person^ 
share  in  the  joint  stock. 

SLVGLE  FELLOWSHIP 

Is  when  different  stocks  are  employed  for  a  certain  equal 
time. 

UuLF.  R^  the  whole  stock  is  to  the  whole  gain  or  loss,  so 
is  each  m:m-s  particular  stock  to  his  particular  share  of  the 
gain  or  loss. 

EXAMPLES. 

I  K  A  and  B  hny  certain  merchandises,  amounting  to  £120, 
of  which  A  pays'£80,  and  B  £40,  and  they  gain  by  them 
£32  ;  what  part  of  it  belongs  to  each  ? 

A  £^;o 

B      40 

As  1^0     •     32      .•      V^^^     Ans.  £21     6     8      A. 

2.  A  ship  worth  G400  dollars  being  lost  at  sea,  of  which  { 
belonged  to  A,  i  to  B,  and  the  remainder  to  C  ;  what  loss 
will  each  sustain,  supposing  they  have  GOOO  dollars  ensured  ? 

Ans.   A's  loss  is  600,  B's  300,  and  C's  lOOu  dolls. 

3.  A  and  B  have  gained  1260  dollars,  whereof  A  is  to 
have  10  per  cent,  more  than  B  ;  what  is  the  share  of  each  ? 

Ans.  A's  060,  B's  600  dolls. 

4.  A  bankrupt  is  indebted  to  A  500  dolls.  37  cts. ;  to  B 
228  dolls.  ;  to  C  1291  dolls.  23  cts.  ;  to  I)  709  dolls.  40  cts. 
and  his  estate  is  worth  but  2046  dolls.  75  els.  ;  how  much 
does  he  pay  per  cent,  and  what  is  each  creditor  to  receive  ? 

Ans.  He  pays  75  per  cent,  and  A's  part  is  375  dolls.  27| 
cts.;  B's  171  dolls.;  C's  968  dolls.  42}  cts.  j  and  D's  532 
dolls.  5  cents. 

5.  Three  boys,  John,  James  and  William,  buy  a  lottery 
ticket  for  3  dolls,  of  which  John  pays  90  cts.  James  1  doll, 
and  William  the  remainder.  This  ticket  is  entitled  to  a 
prize  of  2000  dollars,  subject  to  a  deduction  of  12j  per  cent, 
how  much  is  each  to  receive  ? 

Ans.  John  525  dolls.  James  583  dolls.  33^  cts.  William 
641  dolls.  66|  cts. 


88  DOUBLE  FELLOWSHIP. 

6.  Three  merchaiUs  made  a  joint  stock —  A  put  in  £56^ 
Qs.  8d.  B  £478  5  4,  and  C  a  certain  sum,  and  they  gained 
£373  9  II,  of  which  C  took  toi  his  part  £lI2  11  11; 
required  A  and  B's  (>art  of  the  gain,  and  how  much  C  put  in? 

Ans.  A'sgain  £141  6  8,  B's£ll9  11  4,  and  C  put  in 
£450  7   8. 

7.  Three  men  have  to  share  a  legacy  of  1500  dolls,  of 
which  B  is  to  have  4,  C  |,  and  D  the  remainder;  hut  C  re- 
linquishes his  part  to  B  and  D,  leaving  it  to  be  divided  be- 
tween them,  according  to  their  shares  in  the  whole.  It  i« 
3pequ.red  to  know  how  much  of  the  legacy  B  and  D  receive 
respectively?  Ans.  B's  part  is  lUOO,  D's  5UU  doiis. 

DOUBLE  FELLOWSHIP 
Is  when  the  stocks  are  employed  for  different  times. 
Rule.     Multiply    each   man's  stock  by    its  time,    and  add 
them  together,    then  say — As  the  sum    of  the  products  is  to 
the  whole  gain  or  loss,  so  is  the  product  of  each  man''s  stock 
and  time  lo  his  share  of  the  gain  or  loss. 

EXAMPLES. 

1.  B  and  C  trade  in  company  ;  B  put  in  £950  for  5  months, 
and  C  £785  for  6  months,  and  by  trading  they  gain  £^tl% 
18*.  4'/.,  what  is  each  man's  part  of  the  profit? 

B's  stock  950X5=1750 
C'«    do.    785X6  =  4710 

2.  Two  merchants  enter  into  partnership  for  16  months. 
A  put  into  stock  at  tirst  1200  dolls,  and  at  the  end  of  9  months 
200  dolls,  more  ;  B  put  in  at  tirst  1500  dolls,  and  at  the  ex- 
piration of  6  months  took  out  500  dolls.  ;  with  this  stock  thej 
gained  772  dolls.  20  cts.:  what  is  each  man's  part  of  it  ? 

Ans.  A's  401  dolls.  70  cts.;  B's  370  dolls.  50  cts. 

3.  Two  persons  hired  a  coach  in  Boston,  to  go  40  miles, 
for  ^0  dolls.  With  liberty  to  take  in  "i  more  when  they  pleas- 
ed. Now  when  they  had  gone  15  miles,  they  admit  C,  who 
wished  to  go  the  same  route,  and  on  their  return,  with  n  25 
miles  of  Boston,  they  admit  1)  for  the  remainder  of  the  jour- 
ney. Now  as  each  person  is  to  pay  in  |)ro|>ortion  to  the 
distance  he  rode,  it  is  required  to  settle  the  coach-hire  be- 
tween them. 

Ans.  A  &  B  6  dolls.  40  cts,  each,  C  5  dolls.  20  cts.  D  2  dolls. 


SIMPLE  INTEREST.  89 

SIMPLE  INTEREST 

Is  a  compensation  made  by  the  borrower  of  any  sum  of 
money  to  tiie  lender,  according  to  a  certain  rate  per  cent, 
agret^d  on  for  the  principal  only. 

I'he  leg-al  rate  of  interest  in  Massachusetts  is  6  per  cent. 

Principal  is  the  money  lent.  ^ 

Rate  is  the  sum  per  cent,  agreed  on. 

Amount  IS  the  principal  and  interest  added  together. 

General  Ritle.  Multiply  the  principal  by  the  rate  per 
«ent.  and  divide  the  product  by  100,  and  the  quotient  is  the 
answer  for  one  year. 

KXAMPLE3. 

1 .  What  is  the  interest  of  £496  for  one  year,  at  6  per  cent. 
496 
G_ 

29|76 
20 


151^20 
12_ 

2|40" 
4 


l|oO  Ans.  £29  155.  ftid. 

5.  What  is  the  interest  of  £383  15  9  for  2  years,  at  U 
percent?  383     15     9 

H 


3070       6     0 
191       17    loi 

20      sTol 

32|i2^ 
1243 
12 


6|26 
4 


1)06       £32  125.  Bid.  for  1  year. 


Ans.  65     4  10 J-  for  2  years. 
12 


90  SIMPLE  INTEREST. 

3.  What  will  £826   13     9  amount  to  in  one  year  at  5  per 
cent?  5=:2'^)826   13     9  principal. 

41     G     8i  interest. 


Ans.  £868     0     r^i  amount, 

4.  What  is  the  interest  of  £103   11   4,   for  4  years,   at  7^ 
per  cent  per  annum  ?  Ans.  £31      1      4f 

5.  VYliat  will  £36   14  9  amount   to,  in   three  years,  at  5 
per  cent,  per  annum  ?  Ans.  £42     4   IH 

6.  What  is  the  amount  of  £l 9  15  8,  for  6  years,    at^Gf 
per  cent   per  annum  ?  Ans.  £26     9     2J- 

7.  How  much  is  the  interest  of  £72   12  6,  for  6  months, 
at  6  per  cent,  per  annum  ? 

72   12     6 
6 

4135   15     0 
20 

7115 
12 

1180  £     s.     d. 

4  6  m.  1)4     7     If  for  1  year. 


3|20  Ans.  2     3     6|  for  6  months. 

Note.  When  the  time  is  months,  multiplying  by  the  rate  for  the 
t-ime  gives  the  answer.  This  rate  is  found  by  multiplying  the  time  by 
the  given  rate  per  cent,  for  a  year,  and  dividing  the  product  by  12.  The 
quotient  is  the  rate  required,  and  is  always  equal  to  half  the  months  when 
the  yearly  rate  is  6  per  cent. 

8.  What  is  the  interest  of  £25  19  3  for  8  months,  at  6 
per  cent,  per  annum  ? 

8  months.  25  19     3 

0  4 


12)48  1,03   17  0 

^  '20 

4  rate=half  the  months.  

0,77 
12 


9,S4     Ans.  £10  0. 


SIMPLE  INTEREST.  91 

9.  How  much  will  £o3  9  4  amount  to,  in  20  months,  at 
6  per  cent,  per  annum  ?  Ans.  £58   16     3. 

10.  How  much  is  the  interest  on  a  bond  of  £295  17   10, 
for  1 8  months,  at  8  per  cent,  per  annum  ? 

295   17    10 
18  1 2  the  rate  for  the  time. 


u 

35  50  14  0 

12)144 

20 

12 

10,14 
12 

1,68 
4 

2,72  Ans.  £35  10     1 


11.  How    much    is  the    interest   of  £80  12     9,    for   23 
months,  at  G  per  cent,  per  annum?     .      Ans.  £9    '5     5^ 

12.  iToiv  much  is  the    interest  of  £36   14     9,   from  19th 
May  to  25lh  October,  at  6  per  cent.  ? 

36   14     9  4  m.=i)2     4     1   for  1  year. 

6 


*if,20  8 
20 


0 

14 

H 

1  m.=i  0 

3 

8 

6  d.=:l  0 

0 

,8| 

4,03  Ans    0   19      1 

12 


1,02 
13.  What   will  £l87   14  9    amount  to,  from  11th  June, 
1797,  to  26th  October,  1798,  ut  6  per  cent,  per  annum? 

Ans.  £203  4  5J 
11.   How  much   is  the  interest   of  £l9   13  7  from  3d  Ja- 
nuary, 1797,  to  18th  May,  1798,  at  6  per  cent,  per  annum  ? 

Ans.  £1    12  51 

To  find  the  interest  of  any  sum  for  months^   at  6  per  cent,  per 
anniun^  by  contraction. 

TiiJLK.     Multiply  the    pounds   by  the  number  of  months; 
he  first  or  units  figure  of  the  product  is  pence,  and  the  rest 


92  SIMPLE  INTEREST. 

are  shillings,  obscrvini;::  to  increase  tiie  pence  in  the  product 
hy  i  when  they  exceed  4. 

EXAMPLES. 

15.  What  is  the  interest  oi'£b&  for  1,  5,  7  and  12  months? 

56  56  56  56 

mo.     1  5  7  i2 


.ns.  ba.  Id.             2.-i   Od, 

395.  2^. 

675.  2d. 

16.   £45  for  6  months. 

. 

Ans.  £1     7 

0 

17.    32  4          5 

- 

8     2 

0 

18.      19           7 

- 

-      0   13 

3 

19.     11           1           -          . 

. 

0     1 

1 

//  there  are  shillings^  ^c. 

To  the  pounds  add  the  decimal  of  the  nearest  even  num- 
ber of  shillings  (this  will  be  suoicientiy  exact  for  business) 
and  multiply  by  the  month*  as  before,  separate  two  figures 
of  the  product  to  the  right,  and  the  left  haml  figures  are  the 
shillings,  then  multiply  the  figures  pointed  off  by  12,  and 
the  product,  rejecting  two  figures  to  the  right,  is  the  pence 
♦f  the  answer. 

2       4       6       8        10        12       14       16        18  shillings. 
,1       ,2      ,3      ,4         ,5        ,6         ,7        ,8        ,9  decimals. 
20.  How  much  is  the  interest  of  £347  6  9  for  3  months? 
347,3 
3 

shillings  104,19 

Ans.  £5  As.  2d. 
21  How  much  is  the  int.  of  £195  15  10;^  for  10  monthe  T 
195,8  ,80 

10  12 


shillings  195,80 


Ans.  £9   155.  d^J. 

2,40 
The  Talue  of  the  remainder  is  thus  shewn  to  be  9~d, 


SLMPTE  INTEREST.  95 

J?.  Whnt  is  the  interest  ol  i:590  Id  9f  for  3  years,  7 
monthij  and  19  days? 

£69  1   nearly. 
43 


1773 

23G4 

13  days  }        295 

3           j          59 

1           i          19 

2578, 6-f  1   because  it  exceeds  4.     (See  Rule.) 

£128   IB  7 

23.  How  much  is  the  interest  of  £476  9  8  for  9  months 
aEfli  13  days? 

£476,5 
9 

10  days  ^ 
3  do.    yV 

4288,6 

158,8 

47,6 

449,4t 

Ans.  £tt  9  6| 
24.  Whnt  is  the  interest  of  £40  for  7  years,   5  months, 
and  2^  days? 

40 

89  montbf. 


3560 

IB  day 

•i 

20 

10  do. 

^ 

IS 

I   do. 

tV 

1 

£17 

369,4 

A»s. 

19  h 

n  SIMPLE  INTEREST. 

25.  What  is  the  interest  of  £240  for  50  flays,  at  6  perct.? 

Or  by  Conjpound  ProportiOK* 
240  240 

6  50 


14,40  6083) J  2000(1 

20  6083 


8,00  i9I7 

20 
d. 


dQ5  :  £U  Ss,   :  :  50  :  £1   195.  5id.  6083)118340(19 

6083 


57510 
54747 


2763 
12 


6083)33156(5 
30415 


2741 

4 


60S3)10964(i 
6083 


4881 

Ans.  £1  19  51 

SIMPLE  INTEREST  IN  FEDERAL  MONEY. 

The  principal  given  in  English  money,  and  the  interest 
required  in  federal. 

Rule.  Rod 'ice  the  given  sum  to  shillings,  the  product  gives 
the  answer  in  cents,  and  the  pence  are  mills  nearly — the 
reason  is,  that  at  6  per  cent,  per  annum,  one  fifth  of  a  dol- 
lar is  the  annual  interest  of  a  i)ound — that  is,  20  cents  for  20 
shillings,  or  1  cent,  for  every  shilling  in  any  given  sum. 

EXAMPLES. 

1.  Required  the  interest  of  £194  15  3  for  1  year  in  fede- 
ral money.  194   15  3 
20 

3895  ccuts.  Ans.  2^  dolls.  95  cts.  3  ms. 


SIMPLE  INTEREST.  96 

2.  What  is  the  interest  of  Jt:i29   13  2  for  2  years  in  fede- 
ral money  ? 

129   13  2 


26y3,2  for  1  year. 

2 


5186,1  Ans.  51  dolls.  86  cts.  4  ms. 

3.  What  i»  the  interest  of  £91   12  1  for  5  years,  in  fede- 
ral money  ? 

91   12  1 

20 


1832,1   for  1  year. 


91,605  for  5  years.     Ans.  91  dolls.  60|  el«. 
4.  What  is  the  interest  of  £139   17  2  for  4  months? 
139   17  2 


20 


4  mo.  1  2797,2 


9,32,4  Ans.  9  dolls.  51  cts.  4  ms. 


Principal  in  Federal  Money^  and  Interest  required  in  the  same, 

RuLF,.  Multi|)ly  the  principal  by  the  r:ite  per  ct^nt.  and  as 
you  siinposf^  100  for  a  divisor,  point  oil  the  (pjolient  as  in 
divisioii  of  decimal*. 

The  following  rule  answers^the  same  purpose. 

When  the  principal  is  dollars  only,  multijMy  by  the  rnte, 
and  from  the  product  ponit  otf  two  tig-ures  to  the  rjght,  the 
fiofures  to  the  M\  hand  of  the  point  j^ive  the  answer  in  dol- 
l.us,  and  the  rest  are  d'  cimal  parts  or  cents. 

If  there  are  ceutn.  <^h\  in  the  p^  • -- •  s^  multiply  by  the 
rat'%  and  po-nt  off  a^  ausve.      i':  to  the  ieff  of  tiiC 

po  lU  r '  ^'  th  •  uuw^r  .1)  the  same  nuiiiLi  with  the  lowest  de- 
nommailjii  .n  tue  principal. 


96  SIMPLE  INTEREST. 

EXAMPLES. 

ft.  What  is  the  interest  of  4 1 9  dolls,  for  1  year  at  C  per  tP. 
4i9 
6 


25,14  Ar\9.  25  dolls.  14  cts. 

C.  What  is  the  interest  of  173  dolls.  50  cts.  ibr  1  jear,  at 
6  percent.?  173,50 

6 


cents   1041,00       Ans.   10  dolls.  4t  cts. 
7.  What  is  the  interest  of  327  dolls.  82  cts.  5  mills  for  1 
year,  al  8  per  cent.  ? 

327,82,5 
8 


mills   2'')226,00  Ans.  56  dolls.  22  cts.  6  ms. 

8.  How  much  is  the  interest  of  325  dolls,  for  3  years,   at 
per  cent,  per  annum? 

325  Or  thus,     325 

6  18  rate  for  the  time. 


19,50  for  1  year.  265)0 

3  325 


58,50  for  3  years.  58,50 

Ans.  58  dolls.  50  ctl. 


When  the  time  is  months, 
RuLK.     Multiply  hy  b^jlf  the  number ;  this,  as  wa.a  before 
ohserved,  is  always  equal  to  the  n^te,  for  the  lane-,  vviien  the 
annual  rate  is  6  per  cent,  per  annum. 

EXA>5PfJ.S. 

9.     What  is  the  interest  ot  284  dollars,  for  8  months  at  S 
i^erceot.?  284 

4 

11, oS  Ans.  11  dolls.  36  cts. 


SIMPLE  INTEREST.  97 

It.  How  much  is  the  interest  of  187  dolls.  25  cts.  for  16 
mouths,  at  6  per  cent,  per  annum? 
187,25 
8 


cents  1498,00        Ans.  14  dolls.  98  cts. 

11.  What  is  the  interest  of  95  dollars,  for  2  months,  at  6 
per  cent,  per  annum  ? 

95 

1 

,95  Ans.  95  cents. 

12.  How  much  is  the  interest  of  126  dolls.  46  cents,  for  9 
months,  at  6  per  cent.  ? 

126,46 
44 


5t»5;84 
63,^3 


cents  5n9,07  Ans.  5  dolls.  69  cts. 

13.  How  much  is  the  interest  of  124  dolls,  for  1  montk 
at  6  per  cent.  ? 

i)124  Or      124 
,5 

62,  

,6  -,0  Ans.  62  cts. 

14.  What  is  the  inter^«»t  o^*6  '4  dolls   8  4  cts.  for  if  months 
at  10  per  I'snt.  per  annum? 

694,84  Or  694,84 

10  7rJ=rate  for  the  time. 


cents  694y,i'^  for  a  year.        4863,S8 

347,42 

e     i     3474,2 


5     1     1737,1  cents  52,1  1,30 

^2,11,3  Ans.  52  dolls.  1 1  ctsv  3  me. 

K 


98  SIMPLE  INTEREST. 

15.  How  much  h  the  ftmonnt  of  PrSo  dollars,  for  5  years 
and  8  months,  at  G  per  cent,  per  annum? 
dolls. 
985 
34   half  the  months. 

3940 

2955 


3>4,00  interest. 
9v;5,       principal. 

1319,90  amount.       Ans.   ISIH  dolK  90  ctt. 

When  the   time  is  mon-hs  nnd  dayj*,    nnd  tl  f^  nr.riiol  rate  6  per  cenh 
muUiply  by  k-lf  ^be  r,  •  ;;  -i-:  '    ol'  Ikl  v.   tr^i-]  to 

the  r.*i.e,   for  the  irivei.  =  ■  ■•■:    -   (  .,    \:t  nO\  lor  .i.e 

decimal  in  the  r:<  o,   -    ^    i  .1  ere  Lea  rer-iriider 

in  lakirg  a  sivt]:  of  >    *^  <l      ,  iraciion;  this,  and  not 

^e  decimal,  will  always  give  tiie  exac;  laie. 

EXAMPLES. 

16.  What  is  the  interest  of  194  dolls,  for  4  months  and  12 
^ays,  at  6  per  cent.  ?  * 

194 
m.  VI.  2,2=:to  the  rate  found  hy  the  rule, 

12  :  6  ::  4,4  or  the  annexed  calculation. 

6  388 

388 

12)20,4  

4,26,8 


2,2  Ans.  4  doll3.  26  cts.  8  ma. 

17.  How   much  is  the  interef»t  of  263  dolls.  48  els.  for  2 
months  and  21  da3^s,  at  6  per  cent.? 
263,18 

79044  ^ 

26348 
1  3  i  74 


cents  355,698  Ans.  3  dolls.  55  cts.  6  m?. 


SIMPLE  INTEREST.  99 

18.  How  much  is  the  interest  of  318  dolls,  for  10  months 
^M  16  days,  at  G  per  cent.? 
318 
5,2| 


G3t> 

1590 

^ 

J  06 

i 

1U6 

dolls:   16,74,8  Ans.  16  dolls.  74  cts.  8  ms. 

19.   What  is  the  interest  of  413  dolls,  for  1  year,  7  months 
and  17  days,  at  6  per  cent.  ? 

418  418 

9,7f  5 


2926  6)^090 

3762  

fori  2^^»^=348J.  ^^^* 


^ 


2o9>       _„, 
139^  =348^ 


dolls.  40,89,4  Ans.  40  dolls.  89  cts.  4  m»r 

20.  How   much  is  the  interest  of  268  dolls.  44  cts.  for  3 
years,  5  months  and  26  days,  at  6  per  cent.  ? 

268,44 
20,9^ 


241596 
536880 
8948 


cents  5619,34,4      Ans.  56  dolls.  \9  cts.  3  ms. 
21.  What  is  the  interest  of  1  dollar,  for  18  days,  at  6  per 
«ent.?  1 

,0ii,3  mills.  Ans.  3  mills. 

One  fior,ire  is  sopnratoH  for  the  decimal  in  the  multiplier? 
anrl  two  Ciphers  are  supplied  and  pointed,  according  to  the 
general  rule. 


100  SIMPLE  INTEREST. 

22.  What  is  the  interest  of  910  dolls.  50  cts.  for  5  years, 
5  months  and  26  days,  at  7  per  cent,  per  annum  ? 

910,50  Or  thus,  910,50 

7  22,9i- 


63,73,50  819450 

3  182100 
182100 


1 9 1 ,20,5  for  3  years.  30350 

6  mo.     I     31,86,7  

3  mo.     i    .15,93,3  J)208,80,80iO  at  6per  ct. 

15  days    }       2,65,5  34,80,1 

10  days    |        1,77,0  

1  day     j\        ,17,7  dolls.  243,60,9 


dolls.  243,60,7  Ans.  243  dolls.  60  cts.  8  ms. 

53.  How  much  will  185  dolls.  26  cts.  amount  to,  in  2 years, 
3  months,  and  11  days,  at  7^  per  cent,  per  annum? 

Ans.  216  dolls.  94  cts.  7  ms. 

24.  What  is  the  interest  of  57  dolls.  78  cts.  tor  1  year,  4 
Rionths  and  17  days,  at  4  per  cent,  per  annum? 

Ans.  3  dolls.  19  cents. 

25.  How  much  is  the  «mount  of  2i>8  dnli?.  ^9  cts.  froa 
19th  May,  1797,  to  the  11th  of  August,  1798,  at  8  per  cent, 
per  annum  ?  Ans.  3'ii7  dolls.  98  cts.  4  ms. 

26.  How  much  is  the  amount  of  196  dollars,  from  June 
14,  1798,  to  April  29,  1799,  at  5|  per  cent,  per  annum? 

Ans.  205  dolls.  86  cts. 

27.  What  is  the  interest  of  658  dollars,  from  January  9  i% 
October  9  following-,  at  ^  per  cent,  per  month  ? 

Ans.  29  dolls.   61  cts. 

In  the  calculation  of  interest  in  federal  money;  thus  far,  the  year  is 
.supposed  to  be  12  months  of  30  dayb  each,  making  il  only  360  days. 
Most  persons  use  this  rnelhod  of  computing  the  lime,  but  as  it  is  6  dayf 
less  in  a  year  than  the  ^rue  number,  f  oinc  merclianis  calcul^-iite  by  dayt 
without  any  regard  to  monihs,  a»  being  more  accurate* 


SIMPLE  INTEREST.  101 

EXAMPLES. 

J8.  What  is  the  interest  oi  7086  dollars  for  39  da)^s,  at  6 
per  cent,  per  annum  ? 

By  Compound  Proportion. 
7086 
39 

0  ' 

63774 
21258 

dis.  cts. 

««83) 276354(45  4« 
24332 


33034 
30415 

26190 
24332 

185S0 
18249 

331  Ans.  45  dolls.  48  cfs. 

29,  What  is  the  interest  of  87  dolls.  5(5  cts.  for   72  days 5 
at  6  per  cent,  per  annum  ;' 

87,56 
72 


17512 
61292 

cts.  «*. 

«0S3)6304,32(103  6 
6083 


22  32 
18249 

38830 
36498 


2332  Ans.  1  doll.  3  cts.  6  ms. 

dlls,  cts,      days*  dils.cts.m. 

80.     2962  19  for  254  at  6  per  cent,  per  ann.  Ans.  123  68  8 

31.  35               250       -              -  -  1  47  2 

32.  1733  97  102  -  -  -  29  /  5 
83  45 J  52  47  -  -  -  3  5  9 
84.  215  SO  125  -  -  -  4  43  4 
S5  5.7  90  84  -  -  -  7  15  1 
3«.    73  63    92   -     .  .  1  11  3 

K2 


1©2  SIMPLE  INTEREST. 

The  following  method  cf  ralculat-ng  the  interest  upon  a<> 
oiQunts,  when  there  are  partial  payments,  is  sometimes  uscd- 
1798.  dolls.  days.    prod.princ.'!^-tmie. 


"^January  2,  Lent            100  on 
15,  Lent           110 

int. 

for  13       - 

.       1300 

210 
20,  Received     162 

- 

5 

1050 

48 
February  3,  Lent,           95 

- 

-       14        - 

-       672 

143 
10,  Received    90 

• 

7       - 

-       1001 

53 
16,  Lent           186 

- 

-       6 

-      .318 

239 
26,  Received     70 

- 

-     10 

-      2390. 

169 
March  1,  Lent           250 

• 

-       3 

507 

419 
3,  Received  270 

- 

.       2 

838 

149 
13.  Received  143 

- 

►     10 

149© 

20,  time  of  adjustment,      6       -         -       7        -       -  42 

d.cts.  9608 

Then  6083)9608(   1,57  interest  at  6  per  cent. 
6083    6        th"  p.irjcipal  due. 

35250     7,57  tiie  amount  due  March  20th. 
30415 


48350 
42581 

67*9 


SIMPLE  INTEREST.  lOS 

T5y  this  method  interest  mav  b<*  C'llciilated  on  account?, 
multiulyitii^  eacU  sum  i)V  the  Anys  it  is  at  interest,  and  tak- 
ing" the  quotient  of  36500,  divided  by  the  rat«  per  cent,  as  a 
fixed  vlivisor  to  the  sum  ot'the  product?.  Thus,  the  rate  in 
the  last  example  being-  G  per  c#^nt.  the  divisor  is  6083  ;  l"Or 
6  per  cent,  it  woiiid  be  73oO  ;  for  7  per  cent    5214,  kc. 

It' the  time  is  months,  multiply  each  sum  by  the  months  it 
is  at  interest,  and  take  the  quotient  o\  1  iOO,  divided  by  the 
rate  as  a  divi^sor.  Thus,  tor  6  per  cent,  the  divisor  is  ^2<>0  ; 
for  5  per  cent.  240  ;  for  8  per  cent.  150,  fcc. — [*See  Compound 
Proportion.^ 


m  COMPUTING  lATEREST  OJV  AOTES,  ^^c. 

It  has  2:<^nerany  been  the  custom  to  (ind  the  amount  of  the 
principal  from  the  time  the  interest  commenced  to  the  time 
of  settlemeni,  and  likewise  the  amount  of  each  payment,  and 
then  deduct  the  amount  of  the  several  payments  from  the 
amount  of  the  principal. 


A,  by  his  note  dated  April  25th,  1798,  promises  to  pay  B 
774  doils.  76  cts  on  demand,  with  interest  t©  commence  4 
months  after  the  date.  On  this  note  are  the  following  en- 
dorsements : 

Received,  Oct.  \2th,  \19S,  260  dolls.  19  cts.— Ocf.  13/^, 
1793,  60  doll3.~A*ov.  2,  1798,  200  dolls.  And  the  settlement 
is  made  Dec.  Ibth^  1798. 

CALCni.ATTON^. 

The  principal  carrying  interest  from  25th  Aug.  1798  -  774  76 

Interest  to  Dec.  15,  1798         -         3  m.  20  days.  •  14  2* 


Amount  of  the  principal         -         -         -         *  *              788  9€ 

dlls.  cts. 

First  payment,  Oct.  12,  1798         -         -          -  260   19 

Interest  to  Dec.  15th,  i  798     -     2  m.  3  days.         -  2  73 

Second  payment,  Oct.  13,  1798          -         -         -  60  00 

Interest  to  Dec.  }5ih,  1793  -     2  m.  2  days.           -  0  62 

Third  payment,  Nov.  2,  ;  798           -          -          -  200  00 

Ihlerestto  Dec.  15,  1798,      -     1  m.  13  days.         -  1  43 


Amount  of  the  paymen.s 624  97 


etLlement  is  made  for  .         .         •         ,  ggiu,  2«8  99 


104  3IMPLK  INTEREST, 

RULE  established  by  the  Courts  of  Lazv  in  Massachusetts  for 
tnakiriir  up  j'l'Igments  on  sii^.URi'iiKS  for  monkv,  ivh/ch  are 
upon  vnicrest^  and  on  waick  partial  paynients  have  btea  en- 
dorsed. 

Compute  the  interest  on  the  principal  sum,  from  the  time 
wh.»:i  the  interest  commenc-Ml,  vo  ih2  nrt-t  tiaj<^  wlv^n  a  [^^ly- 
ment  was  mnie,  which  exc<'  '    n.  :^,e  r-  <^n. 

with    the  preceding- puvm.  ;.>;    i!;e    .  at 

time  due;'  add  thai  iuleft-si  to  liie  jMin;  j>aU  aii.i  from  the 
sura  .Subtract  the  payment  m-i  je  u  ili.jt  tiru  .,  together  with 
the  preceding  payments  (ifai)};  aiid  ihe  rema  luier  torn;s  a 
new  princip.il  ;  on  which  compute  and  sp.btract  tlie  interest, 
as  upon  the  tiist  principal  :  an.i  f>roc-?ed  in  this  maaner  to 
the  time  of  the  jii  i;^ment.  iiy  Jh:s  rule,  ihe  payments  are 
first  applied  to  keep  dovvo  the  in-yrest ;  and  no  part  of  the 
interetjt  ever  ibrms  a  part  oi  a  praicipal  carrying  interest. 

The  following  example  wdl  illustrate  the  rule,  in  whick 
the  interest  is  computed  at  the  rate  of  6  per  cent,  by  the 
year,  ihat  being  the  legal  rate  of  interest  in  jMassachusetts. 

A,  by  his  note  dated  Jan.  I,  17 HO,  promises  to  pay  to  B 
lOUO  dolls,  in  6  ^nonths  from  the  date,  Avith  interest  from 
the  date.     On  this  note  are  the  following  endorsements  : 

Received,  Jipril  1,  178Q,  24  dolls. — flugust  I,  1780,4  dolls. 
Dec.  1,  1780,  6  doJJs.  — Fe6.  I,  1781,  60  dolls.— J«/i/  1,  1781, 
40  dolls.— /imc  I,  1781,  300  dolls.— 5e/>/.  1,  1784,  12  dolls. 
— 7rni.  K  1785,  J  5  dolls.— Oc^  1,  1785,  50  dolls.  And  the 
judgment  is  to  be  entered  Dec.  1,  lldQ. 

CALCULATION. 

dlls.  ct» 
The  principal  sum  carrying  interest  from  January  1,  17S#,  1000  GO 

Interest  to  Apnl  1,  1780,  '6  months         .         _         -  -  15  00 

Amount     1015  00 
Paid,  April  1,  17S0,  a  sura  exceeding  the  interest         -  -         24  00 

Remainder  for  a  new  principal 991   0§ 

Interest  on99i  dlb.  from  April  1,  178©,  to  Feb.  1,  1781,  10  mo.  49  55 

Amount     1040  5I» 
Paid  Aug.  1,  1780,  a  sum  less  than  the  interest  then  due    ^'4  00 
Paid  Dec.  1,  17S0,  do.  do.  6  00 

Pfiid  Feb.  1,  17«i,  do.  greater  ihaa  the  interest  then  due     60  00 

79  Of 


SIMPLE  INTEREST.  Ids 

dlh.  cts. 
Remainder  fbr  a  new  principal         -         -         -         _         .  97O  55 

Inte.est  0.1  070  dolls.  55  cts.  from  Feb.  1,  1781,  to  July  1, 

1781,  5  months         -         -         -         -         *         -         -  24  2fi 


Paid  .July  1,  1781,  a  sum  exceeding  the  interetrt 


Amount     994  81 
40  Of 


Remainder  for  a  new  principal         -         -         -         .         •  954  31 

Interest  on  954  doHs.  81  cts.  from  July  1,  1781,  to  June  1,  1784, 

2  years  11  months.         -         -         -         •         -         -         -        167  Of 


Paid  June  1,  1784,  a  sum  exceeding  the  interest 


Amount     1121   90 
300  0« 


Remainder  for  a  new  princip.il         -----  821  9t 

Inierest  on  82    dolN.  90  cts.  from  June  1,  1784,  to  Oct.  1, 1785, 

1  year  4  months         -         -         -         -         -         -         --65  75 

Amo'jnt     887  %h 
Paid  Sep.  1,  1784,  a  sum  less  than  the  interest  then  due  $; :  2  00 

Paid  Jan.  J,  1785,  do. 16  00 

Paid  Oct.  1,  '785,  do.  greater  with  two  last  payments 

than  interest  then  due         -         -         *  -         -         50  00 

77  60 


Remainder  for  a  new  principal  -         -         •         •         -  810  65 

Inicrert  on  SO  dalU    £>5  cti-.  from  Oct.  T,  1785,  to  Dec.  1,  1790, 

the  time  when  judgment  is  to  be  entered,  6  years  2  months         251   3t 


Judgment  rendered  for  the  amount 


1061  9S 


A  TABhE^  sheiioing  the  number   of  days ^  from  any  day  in  any 
months  10  the  same  day  in  any  other  mnath  through  the  year. 


From  Tan.  Feb,  M.  Ap.Ma.Jun.  Jul.  Au.Sep.  Oc.  No.De. 
t'o~j"an.l365|334|3b6J2>5|245  214|184|753iT22r92|  61|Tl 


~FV^|  3'iJ865lir37i¥06|276g 
'^^M^|"~^Ts|;}65|334:a(M^  90 

April.f90|  59|  3  ?  J365 ;335!304|274:24i^272| » 82|  i 5 1 1 !  2 1 

^^Ma^72bT]8^  2|  i  sTjTsT 

June.fi  5  l]T20!  92j_6 1 1 " 3Jl|365L^^!30 iT273!243]2T 2|"^2 
~Ji7I7r;'l8]|150| r22j~9if61|"  30j365[384 jOOir 273Vl2J2 12 
"  Au^-|2 1 2iT8  I|"r53r<22}  92|'6 1|  3i]3<a5|334|304!27h,243 
■  SepL|24"3i^'2!~84J^5^^ 

"0^!2r :;;242;2  i 4i7_83|  ^._53i  ■  22|  92|" elj' 36[365l3.34[304! 
^^|304,27>.;246j2Hlp^  \b^]2^^  92ij6_''|  3"M3G5;3:^| 
"l^ec.|334S03;275|244|2i4|l83h53|{  22"|T:|'"6"r|~30J365| 


106 


COMPOUND  INTEREST. 


THK    USK    OF    THE    TABLE. 

Suppose  the  number  of  d.iy«  between  the  3(1  of  M?iy  ani 
the  5(1  of  November  vras  required  ;  look  in  the  coiiiTnn  nnder 
May  tor  November,  and  ag-am^t  that  month  you  will  lind  184. 

It'ihe  sfiven  dnvs  be  different,  it  is  only  adding  or  snb- 
traciinq;  rhpir  inequality  to  or  from  the  tabular  nnmbi^r. — 
Th.is,  from  May  3d  lo  Nov.  17th  h  184  +  14=198  days,  and 
from    Nov.    nth  to  May  rkl  is  i  d  I  — 14—16  7  days. 

If  the  time  exceed  a  year,  365  day?  must  be  added  ;  thus 
Ir-.-.a  i:;e  Uh  cl  February,  1798,  to  the  4tb  of  ^ept.  1799,  ii 
2;  ;-f 3^5-:'i77  d^vs. 

Np.te.  la  leip  -  enr-,  if  the  end  of  the  month  of  February  be  in  th« 
time,  Oiie  day  ma^i  oe  adde<l  on  that  account. 


COMPOUND  INTEREST 

ts  that  which  jHsos  both  from  the  principal  and  interest; 
that  ^'s,  when  the  interest  on  m -ney  becomes  due,  and  not 
paid.  It  IS  added  to  the  prhicipal,  and  intere8t  is  calculated 
on  th5s  a!))0!]nt  a^  on  the  principa]  before. 

Rule.  Find  the  simple  interest  of  the  given  sum  for  one  year,  and 
odd  to  it  the  principd,  a -d  -.hen  find  ih**  iniere'-t  for  ihat  amount  for 
the  jiex'  year,  aad  so  ou  for  .he  number  of  years  required.  Subtract  th« 
pri,  » ipd  from  the  last  amount^  and  the  remainder  will  be  the  compound 
interest. 

EXAMPLES. 

1.  What  is  the  interest  of  £246  14#.  Qd.  for  3  years,  at  i 
per  cent,  per  annum? 


24ti    14  6 

12     6 

2     9 


1 
¥ 


261 
13 
?   1 


^  >  first  year's  interest. 
64  amount  of  the  first  year. 
9  of  /    second  year's  interest. 


10  6 


277     4    l-{-  amount  of  the  second  year. 
13   17  2^  " 


2    15   51 


third  year's  interest. 


2V)3  17  V  amount  of  the  third  year. 
216    H   6  first  principal. 


47     2  6  compound  interest  for  3  years. 

Ans.*£47  2  6 
S.  What    is    the    compound    interest  of  i^76o    lO     for  4 
y^ars,  at  6  percent,  per  aauum?  Aas.  j^lC^  12  3i 


€OMPOUND  INTEREST. 


107 


3.  How  much  is  tho  Mmonnt  of  £  1 28   17 j.  6^/.  for  0  years, 
at  8  p(^r  ct.  fxM- annum,  eo.'n?)0'inv1  inttresl?   Aiis.    182   i6  2f 

4.  How    mnch   is  th*^-  -^monn*  of  500  uolh»rs,   for  3  jeai^, 
at  6  per  cent,  per  annum,  i  ifiierest? 


?0 

X 


500, 


iir^t  interest. 


5 

I 


1 
3 


530, 
•iife^SO 
5,00 

56 1 ,80 
2 


second  interest. 


s,09     > 
5,(51,8  ^ 


third  interest. 


I  595,50,8  um't  req.    An-.  §^5^5  50  cts.  R  ra. 
B.  What  13  the  amount  of  62tj  dolls,  ior  7  years,  al  i>  per 
tent,  per  annum,  compound  mLerest? 

Ans.   945  dolls.  78  c!s.  3  ms. 
6.  How  mnch  is  the  compound  inierc^t  ot   1^56  doiis.  for 
15  year?,  at  6  per  cent,  per  aonvmi  ? 

An-'.    1  754  dolls.  ^  ct^.  f^  ms. 

A  TABLE  shewing;  ^T-"  amo^int  of  one  potirid  or  one  dollar  for  any 
number  of  years  under  S3,  at  the  rates  of  6  and  b  per  centy  per 
aniiuiny  compound  interest. 

|Fears.|  ~'  6       Rates.     6  Years.  \ 


1 

l,or>000 

2 

I,i0:r50 

3 

1,^5   (2 

4 

1,2. 5u0 

5 

1,27028 

6 

l,^i  009 

7 

J,M)7   0 

^ 

■,1.7  M 5 

*'. 

,v  1.^2 

.  v) 

;,<>:ssf) 

i  i 

(,/  O.il 

•  2 

S;;^.>^t) 

^3 

i,>^>=:r)65 

14 

l,s:9<>3 

J  5 

2,0/^92 

6 

2,.82S7 

1,00000 

],'2;:60 

],:5)     01 

l,.2o2i7 
1,33 -^^2 
1, 4; 852 
l,c0.363 
7,5'jaS4 

!,7:)0:^4 
KSJ>'-2<) 
2,0  2  .9 
2,  3202 
2,2f0.90 
2,^i96j5 
2,51035 


17 
18 
19 
20 
2i 
22 
23 
24_ 
"25 
2G 
27 
2S 
29 
GO 
3i 
32 


2,29201 
2,-J0c62 

2,b2(;96 
2,65329 
2,78696 
2,92i;:^« 
3,0 

Ir'-'  _ 

3,38^o5 
3,?'5i>67 
3,7bM5 
3,920  3 
4,  6:3 
4,12  94 
4,53804 
4,76494 


Rate>i.     6 

~2,6P277~ 
2,«5434 
3,02559 
3,20753 
3,3Jiy56 
3.f,0353 


4,29 !S7 
4,:  4938 
4,S22S4 
5,-  *  .68 
6,4:838 
6,74349 
*6,088  0 
6,45r>.^S 


i'he  une  of  Jiis  faWe  i  plain  Aiid  easy:  for,  iiiultip!  i  Tg  tiio  figure* 
itandisj  rtr:vi;nr,  tj.»»  number  of  years,  by  the  given  priiiCipai,  the  product 
if  the  ^inoaul  required. 


1#8  (TOMPOUND  INTEREST. 

7.  What  is  the  amoiint   of  50o  doihu's,   ior  3  years,  at  6 
per  cent,  compound  interest  ? 

1,19101   the  tabn'c^r  r;imib<^r  for  ihe  time. 
50U  the  jjiinc  pui 


5lj5,5U500 

Ans.  595  dnJls.  50  cts.  5  ms. 
8.  A  merchant,  on  in?pectfng-  sonie  -^id  acccujJs  in  March, 
1799.  fih.ie  a  ^^etilemi^nt  dated  i-Vlaich,  J 77  I,  i*;  v.  >;  ri*  »i  ap- 
pears liicre  is  dne  ironi  h:m  lo  A  B  £,2  Bs. ;  ll.i  ^  \:iu  he  pays 
w.ih  compound  inter. -si  at  6  per  com.  per  annum.  Ihe 
amount  of  it  is  reqniret-  ? 

5,11  Mo   .'.t   tabular  number  for  2^1  yetirs. 

';i,i  the  principal  with  tbv  shiiiings  inserted 

* decimaiiy. 

2044672 
10i!i:33U 


20 


5.  fevJ^o:- 10 
12 

4 

^r.  1,3)0720 

ln».  XI 2  5^.  ^^J.  or  40  dolls.  09  cU.  3  ms. 

Calculated  in  Fe/hral  Money. 
5,11168 

§  dollars. 

/rfo//*.  -10,^9. '44 

Ans.  40  dolls.  €9  cts,  3  mills,  as  above. 


COMMISSION  AND  BROKERAGE.  109 


COMMISSION  AND  BROKERAGE 

Are  compensations  to  Factors  and  Brokers  for  their  res- 
pective services. 

The  method  of  operation  is  the  same  as  in  Simple  Interest. 

■^^-'  EXAMPLES. 

1.  What  is  the  commission  on  £596  18  4,  at  6  percent.? 
596  18    4  Or  thus,  £5  |  ^\  \  596  18     4 

6  

Mi!    29  16  11 

35|81    10    0  6  19     ^ 


£35  16     U 


20 

16|30 
12 

3|60 
4 

2|10  Ans.  £35  16  3 J 

2.  What  is  the  commission  on  1974  dollars  at  5  percent.? 
1974 
5 


98,70  Ans.  98  dolls.  70  cts. 

3.  What  is  the  commission  on  £526   11   5  at  3i  per  cent.  ? 

Ans.  £18  8  7 

4.  What  is  the  commission  on  £l25b  17  3  at  7§-  per  cent.? 

Ans.  £93  3  \\ 

5.  What  is  the  commission  on  2176  dolls.  50  cents,  at  2^ 
percent.?  Ans.  54  dolls.  41  cts  2  ms. 

6.  The  sales  of  certain  goods  amount  to  1873  dolls.  40  cts. 
what  sum  is  to  be  i-^ceived  for  them,  allowing  2-^  per  cent, 
for  commission,  and  \  per  cent,  for  prompt  payment  of  the 
neat  proceeds?  Ans.  1821  dolls.  99  cts.  9  ms. 


no  COMMISSION  AND  BROKERAGE. 

7.^  Required  the  neat  proceeds  of  certain  goods  amounting 
to  £456   1 1   8,  allowing  a  commission  of  2^  per  cent. 
£5     5V  I  456   11   8 

2J    i    I    22   16  7  commission  at  5  per  cent. 

11     8  3i  commission  at  2j  per  cent. 

Ans.  £445     3  4j  neat  proceeds. 
What  is  the  commission  on  £1371   9  5  at  5  per  cent? 

Ans.  £t^8    jl   5J 

9.  What  is  the  commission  on  £1958  at  bj  per  cent.  ? 

Ans.  £U>7   13  9} 

10.  What  is  the  commission  on  £1859  7  6  at  |  per  cent.  ? 

Ans.  £16  5  4^- 

11.  W'hat  is  the  brokerage  on  1853  dolls,  at  |  per  cent.  ? 

Ans.   13  dolls.  89  cts.  7  ms. 

12.  What  is  the  brokerage  on  £874   15  3  at  {  per  cent.? 

Ans.  £2  3  8| 

13.  What  is  the  brokerage  on  1298  dolls.  53  cts.  at  |  per 
cent.  ? 

1298,53 
3 


8)3895,69 

dolls.  4,86,94         Ans.  4  dolls.  86  cts.  9  ms. 

14.  What  is  the  brokerage  on  £l321  U  4  at  IJ-  per 
cent.?  Ans.  £14   17  4 

15.  A  factor  receives  988  dollars  to  la\  out,  fifter  having 
deducted  his  commission  of  4  per  cent,  how  much  will  re- 
mam  to  be  laid  out  ? 

d. 

100 

4 


If     104  :   100  : :  988  :  950  dolls,  the  answer. 
16.  A  factor  has  in  }\'\<  hrinds  3G90  dollars,  which  he  is  di- 
rected to  lay  out  in  i»^<   >.    r-^^nvinir  fp'un  li  his   commission 
of  2*  percent,  on  the  pLi   h;ise  ;  the  iron  bcvin^:  95  dolls,  per 
ton:  how  much  did  he  [:nr<  h^^'^e  ? 

Ans.  37  tons.  17  ewt  3  qrs,  I6j\  lb. 


INSURANCE.  Ill 

INSURANCE 

Is  an  exemption  from  hazard,  by  paying  or  otherwise  se- 
curing a  Cf^rtain  sum,  on  condition  of  being  indemnified  for 
loss  or  damage. 

Policy  is  the  name  given  to  the  instrument,  by  which  the 
contract  of  indemnity  is  effected  between  the  insurer  and  in- 
sured. 

Average  loss  is  5  per  cent.;  that  is,  if  the  insured  suffer 
any  loss  or  damage  not  exceeding  5  per  cent,  he  bears  it 
himself,  and  the  insurers  are  free. 

Rule.     The  method  of  operation  as  in  interest. 

EXAMPLES. 

1.  What  is  the  premium  of  insuring  £924  at  7  per  cent.  ? 

Ans.  £64   13  7 

2.  What  is  the  premium  on  1650  dollars  at  12  per  cent.  ? 

Ans.    198  dolls. 

3.  What  is  the  premium  of  insuring  1250  dollars,  at  1^ 
per  cent.  ?  Ans.  93  dolls.  75  cts. 

4.  What  is  the  premium  of  insuring  4500  dollars,  at  25 
per  cent.  ?  Ans.  1125  dolls. 

5.  What  is  tlie  premium  of  insuring  1650  dollars,  at  15J 
per  cent.  ?  Ans.  255  dolls.  75  cts. 

6.  What  is  the  premium  of  insuring  1873  dollars,  at  |  per 
cent  ?  Ans    2  dolls.  34  cts.  1  m. 

7.  What  sum  is  to  be  received  for  a  policy  of  1658  dolls, 
jdeducting  the  premium  of  23  per  cent.? 

Ans.   1276  dolls.  6Q  cts. 

8.  What  sum  must  a  policy  be  taken  out  for,  to  cover 
1800  dollars,  when  the  premium  is  10  per  cent.? 

100  Policy. 
10  Premium. 

d.        d,  d. 

90  sumcovered.  If  90  :   100  ::   1800  Ans.  2000  dolls. 
Proof     20U0  dollars  at  10  per  cent. 
10 


200,00  the  policy         2000 

the  premium      200 


sum  covered     1800  dolls. 
9.  What  sum  must  a  policy  be  taken  out  for,  to  cover  392^ 
ddls.  7  cts.  whon  the  prcm^um  is  6  per  cent.  ? 

Ans.  4176  dolls.  67  ct?; 


112  GENERAL  AVERAGE. 

GENERAL  AVERAGE. 

Whatever  the  master  of  a  ship  in  distress,  with  the  advice 
of  his  officers  and  sailors,  deliberately  resolves  to  do,  for  the 
preservation  of  the  whole,  in  cutting  away  masts  or  cables, 
or  in  throwing  goods  overboard  to  lighten  his  vessel,  which 
is  what  is  meant  by  jettison  or  jetson,  is  in  all  places  per- 
mitted to  be  brought  into  a  general  average,  in  which  all, 
who  are  concerned  in  ship,  freight  and  cargo,  are  to  bear  an 
equal  or  proportionable  part  of  the  loss  of  what  was  so  sacri- 
ficed for  the  common  welfare  ;  and  it  must  be  made  good  by 
the  insurers  in  such  proportions  as  they  have  under  written. 

EXAMPLES 

Of  Adjusted  Averages, 
1.  A  loaded  ship  met  with  such  bad  weather,  that  the 
master  and  mariners  found  it  impossible  to  save  her  without 
throwing  part  of  her  cargo  overboard,  which  they  are  au- 
thorized to  do  for  preservation.  Being  thus  necessitated^ 
they  threw  such  goods  as  lay  nearest  at  hand,  and  lightened 
the  ship  of  10  casks  of  hardware,  and  40  pipes  of  Madeira 
wine,  which  they  judged  sufficient  to  keep  her  from  sinking. 
Soon  after  that,  the  ship  arrived  at  her  destined  port,  and 
then  an  average  bill  was  immediately  made  in  order  W  ad- 
just the  loss,  and  to  pay  the  proprietors  of  those  goods  which 
were  thrown  overboard  for  the  good  of  the  whole. 

Average  accruing  to  ship ''^for  goods  thrown  overboard  for 

preservation  of  ship^  freight  and  cargo. 

Ship  valued  at           -             -             -  doUs.  12,000 

Freight  (wages  and  victuals  deducted)  3,000 

Thomas  Nugent's  value  of  goods         -  -  4,000 

Thomas  Morgan's  value  of  goods         -  -  2,500 

.fames  Simpson's  value  of  goods           -  -  8,500 

Andrew  Wilson  for  40  pipes  of  wine  -  "  4,000 

Laurence  Ward  for  10  casks  of  hardware  -  6,000 

40,000 
Mr.  Andrew  Wilson's  goods  thrown  overboard  valued  at  4,000 
.!\Ir.  Laurence  Ward's  do.         -  -         6,000 

^      10,000 

If 40,000  give  10,000  loss,  what  loss  will  100  give? 

Ans.  25  per  cent. 


GENERAL  AVERAGE.  Hi 

The  ship  must  pay  to  A.  W.  and  L.  W.  for  12000 

dollars,  at  25  per  cent.           .          -           -          -  3000 

The  I'reight  3000  dollars,  at  the  same  rate         -  760 

Thomas  Nuj;ent,  (or  4000  dollars,  at  the  same  rate  1000 

Thomas  Morgan,  for  !^oOO  dollars,  at  the  same  rate  625 

James  ISimpson,  for  8500  dollars,  at  the  same  rate  2125 


A.  W.  and  L.  W.  receive  of  the  owners  of  the 
goods  saved,   and  the  ship's  owners  -  -  7500 

Their  property  being  insured,  the  underwriters 
pay  them 2500 


10,000 
2.  The  Sea  Horse,  Capt.  Dix,  laden  with  hemp,  cordage 
and  iron,  bound  from  Riga  to  Boston,  ran  on  shore,  comuig 
through  the  grounds  at  Elsineur.  I'he  captain  hired  a  great 
number  of  men,  and  several  lighters,  to  lighten  the  ship, 
and  to  get  her  afloat  again,  which  was  done  ;  but  he  was 
obliged  to  pay  409  dolls.  23  cts.  for  their  assistance.  This 
expense  being  incurred  to  preserve  both  ship  and  cargo,  the 
average  must  consequently  be  general.  When  the  ship  ar- 
rived at  Boston,  the  captain  immediately  made  a  protest  and 
an  average  bill,  which  was  thus  stated  : 
Average  accruing  to  the  ship  Sea  Horse^  from  Riga  to  Boston^ 

in  nij9,  fur  assistance  in  getting  off  the  strand  of  Elsineur. 
For  sundry  charges  paid  at  the  sound  for  lighters 

and  assistance  in  getting  oif  the  ship  dolls.  409  23 

Protest  and  postage  ---;..  35  37 


The  ship's  freight  money 

Wages  for  all  the  people,  4  ms.  and  20  d.     560  > 

Victuals  for  do.         -         -        -         - 


The  ship  Sea  Horse  valued  at 
Fre  ght  valued  at 

William  Jenkins  for  value  of  hemp 
Daniel  Jones  for  value  of  cordage 
Enoch  Flinu  for  value  ol  iron 

L2 


444  60 

- 

3460 

bO  j[ 

Dot; 

860 

2600 

. 

12000 

- 

2600 

- 

18000 

. 

4000 

2400 

dolk. 

3C»U00 

114  BUYING  AND   SELLING  STOCKS. 

If  39000  dolls,  lose  444  dolls.  60  cts.   what  will   100  dolk 
lose?  Ans.     1  d^I.  14  cts. 

The  ship  must  bear  1 2000  dls.  at  1 1 4  cts.  per  1 00  dls.     1 36  80 
The  freight  2600  dolls,  at  the  same  rate  29  64 

William  Jenkins  for  18000  205  20 

Daniel  Jones  for  4000  45  60 

Enoch  Flinn  for  2400  27  36 


dolls,  444  60 


BUYING  AND  SELLING  STOCKS. 

Stock,  in  the  sense  in  which  it  is  here  used,  is  a  fund  es- 
tablished by  government,  or  individuals  in  a  corporate  ca- 
pacity, the  value  of  which  is  variable. 

EXAMPLES. 

1.  What  is  the  amount  of  1565  dollars  national  bank  stock, 
at  134  per  cent.  ? 

1565 
134 


6260 
4695 
1565 


2097,10  Ans.  2097  dolls.  10  cts. 

2.  What  is  the  amount  of  2958  dolls,  bank   stock,  at  25 
per  cent,  advance  ? 
2958 
25     i     739,50 


3697,50                 Ans.  3697  dolls.  50  cts. 

dolls. 

dolls,  cts. 

3. 

6959  of  8  per  cent,  stock  at  1 10  per  ct.     Ans.  7654,90 

4. 

1796 

6            -           -         9U         -         -          1643,34 

5. 

1284 

3     -           .           .    54^     -        -           .     696,57 

6. 

3172 

deferred         -           89           -         •         2823.08 

7. 

1518 

slate  notes     -           83f     -         -         -    1271,32| 

8. 

16d6 

Union  Bank     •128        -        -        2158,08 

DISCOUNT.  lift 

DISCOUNT 

Is  the  abating  of  so  much  money  to  be  received  before  it 
is  due,  as  that  money,  if  put  to  interest,  would  gain  in  the 
same  time  and  at  the  same  rate. 

Thus  100  dollars  would  discharge  a  debt  of  106  dollars 
payable  in  l!iJ  months,  discount  at  6  per  cent,  per  annum,  be- 
cause the  100  dollars  received  would,  if  put  to  interest,  re- 
gam  the  6  dollars  discount. 

Rule.  As  100  dollars,  with  the  interest  for  the  given 
time,  is  to  100,  so  is  the  given  sum  to  the  present  worth,  and 
the  difference  between  the  present  worth  and  the  given 
sum  is  the  discount. 

EXAMPLES. 

1.  What  is  the  present  worth  of  450  dolls,  due  in  6  months, 
discount  at  6  per  cent,  per  annum  ? 
6  w.  I     6 

3 
100 

103  :  100  ::  450     Ans.  436  dolls.  89  cts.  3  m. 
^.     How  much  is  the  discount  of  £308   15^.    due  in   16 
months,  at  8  per  ct.  per  annum?  Ans.  j£33  1   7f 

3.  What  is  the  present  worth  of  5150  dolls,  due  in  4i 
months,  discounting  at  the  rate  of  8  per  cent,  per  annum,  nnd 
allowing  1  per  cent,  for  prompt  payment?     Ans.  4950  dolls. 

4.  A  is  to  pay  5927  dolls,  on  the  19th  of  April,  17^)9, 
and  5389  dolis  on  the  19th  of  July  following:  it  is  required 
to  know  how  much  money  willdi.scharge  both  sums  on  the 
1 9th  of  January,  1799,  discounting  at  8  per  cent,  per  annum  ? 

Ans.   11569  dolls.  43  cts.  7  m». 

Though  the  discount  found  by  the  preceding  method  is 
thought  to  be  the  sum  that  should  be  deducted  lor  the  pres- 
ent payment,  in  justice  to  both  parties,  yet  in  businese  the 
interest  for  the  time  is  taken  for  the  discount. 


116  DISCOUNT. 


EXAMPLES. 

5.  What  ready  money  will  discharge  a  note  of  150  dollars^ 
due  in  60  days,  ailowing  legal  interest,  or  6  per  cent,  per 
annum  as  discount? 

150 

Irshalf  the  months. 

150 

150  the  debt. 

1,50  the  interest. 


148,50  Ans.  148  dolls.  50  cts. 

6.  Bought  goods  to  the  amount  of  950  dollars^^at  9^  days 
credit,  what  ready  money  will  discharge  it,  allowing  the  m- 
terest  for  the  time  at  6  per  cent,  per  annum  as  discount? 
Ans.  9J5  dolls.  75  cts.  if  calculated  for  3  months. 
935  dolls  95  cts.  if  calculated  for  90  da^'s. 

When  the  interest  for  the  time  is  allowed  as  discount,  it 
is  presumed  that  neither  party  suffers  any  loss,  but  the  fol- 
lowing statement  evinces  the  contrary. 

A  owes  B  100  dollars  payable  in  12  months,  for  present 
payment  of  which  B  allows  6  dollars  or  the  mterest  for  the 
time,  and  receives  94  dollars  ;  this  sum  he  immediately  lends 
to  C  for  the  same  space,  of  time,  and  then  receives  the 
amount,  being  99  dollars  64  cts,  which  is  36  cents  less  than 
he  would  have  to  receive  from  A,  had  he  left  the  money  in 
his  hands;  but  if  he  had  allowed  A  the  discount,  and  not  the 
interest,  for  the  time,  he  would  have  received  from  him  94 
dollars  J4  cents,  and  this  sum  being  put  to  interest,  would 
amount  to  100  <it)ils.  in  one  year,  which  shows  that  the  dis- 
count, and  not  the  interest,  is  the  just  deduction  for  prompt 
payment. 

But  when  discount  is  to  be  made  for  present  payment 
without  any  regard  to  time,  the  interest  of  the  sum,  as  calcu- 
lated for  a  year,  is  the  discount* 


DISCOUNT.  117 


EXAMPLES. 

7.  How  much  is  the  discount  of  853  dolls,  at  2  per  cent,  t 
853 
2 


*      dolls.  17,06  Ans.  17  dolls.  6  cts. 

8.  How  much  money  is  to  be  received  for  985  dolls.  75 
cents,  discounting  4  per  cent.  ?  Ans.  946  dolls.  32  cts. 

BAJVK  mSCOUNT. 

The  method  used  among  bankers,  in  discounting  notes,  &c. 
is  to  find  the  interest  of  the  sum,  from  the  date  of  the  note  to 
the  time  when* it  becomes  due,  including  the  days  of  grace; 
the  interest  thus  found  is  reckoned  the  discount.  Thus,  if  a 
note  for  100  dollars,  dated  the  2d  September,  be  discounted 
at  a  bank,  for  30  days,  the  interest  of  that  sum  for  33  days, 
being  55  cents,  is  deducted  for  discount.  It  may  be  asked, 
why  interest  for  33  days  is  calculated  on  a  note  for  30:  the 
answer  is,  that  as  custom  has  allowed  the  borrower  three 
days  of  grace — that  is,  though  the  time  of  the  note  expires 
on  the  1st  of  October,  (the  day  of  the  date  being  included  in 
the  30  days)  he  may  withhold  the  payment  till  the  4th — it  is 
therefore  reasonable  that  he  should  pay  interest  for  it. 

tf  a  note  of  100  dollars  were  discounted  at  a  bank  for  60 
days,  the  interest  of  that  sum  for  63  days,  being  105  cents, 
would  be  deducted  for  the  same  reason. 

In  case  payment  of  a  note  be  not  convenient  at  the  proper 
time,  a  new  note  must  be  presented  on  the  day  of  discount, 
immediately  preceding  the  expiration  of  the  time,  paying 
the  same  discount  or  interest  for  the  time,  as  before  stated. 
Thus,  a  note  of  100  dollars,  dated  October  7th,  1800,  for  30 
days,  though  it  is  not  payable  till  November  8th,  yet  must 
be  replaced  by  a  new  note  on  Tuesday,  Nov.  4th,  paying  at 
the  same  time  55  cents.  A  note  of  the  same  date,  for  100 
dolls,  for  60  days,  though  not  payable  till  Monday,  Decem- 
ber 8th,  (includmg  in  this  time  the  days  of  grace)  must  be 
replaced  by  a  new  note  on  Tuesday,  December  2d,  paying 


118  DISCOUNT. 

likewise  105  cents.  In  the  former  case  the  borrower  sui- 
tains  a  loss  of  5  days  in  30,  and  in  the  latter  7  days  in  60,  hj 
renewing.  All  Banks  have  their  stated  times  of  discount, 
generally  once  a  week.  In  the  preceding  cases,  the  Bank 
is  supposed  to  discount  on  Tuesday.  Some  Banks  discouat 
twice  a  week,  others  oftener. 

The  discount  of  any  sum,  discounted  for  30  or  60  days,  is 
found  by  multiplying  it  by  one  sixth  of  the  days.  [See  Inter- 
est^  page  98. 


EXAMPLES. 

1 

1.  1 

Flow  much  is  the  interest         2.  What  is  the  interest  of 

of  2.^8  dolls,  discounted  for  30     564  dolls,  discounted  for  60 

days ! 

days? 
238                                            564 

,5i=^  of  33  days.               l,0i: 

=^  of  63  days. 

1190                                        5640 

119                                           282 

1,30,9                                       5,92,2 

Ans.   1  doll  30  cts.  9  m.      Ans. 

5  dolls.  92  cts.  2  m. 

What  is  the  discount  of  the  following 

sums,  viz.    ' 

dolls. 

dls,  cts.  ms. 

3. 

1 59  discounted  for  30  days. 

Ans.  0  87  4 

4. 

273        -         -         do. 

1    50   1 

5. 

683        -         -         do. 

3  75  6 

6. 

789        -         .         do. 

4  33  9 

7. 

2194        -         -         do. 

12  06  7 

8. 

21 9  discounted  for  60  days? 

Ans.  2  29  9 

9. 

187        -         -         do. 

1    96  3 

10. 

319        -         -         do. 

3  34  9 

11. 

658        -         -         do. 

6  90  9 

n. 

2169        -         -         do.         - 

22  77  4 

DISCOUNT.  119 

13.  How  much  is  the  discount  of  a  debenture  of  319  dolls. 
payable  in  210  days,  discounting  for  30  days  ? 

Note.     28  days  are  allowed  for  a  month,  interest  being 
calculated  as  if  the  note  were  renewable. 


28)210(7  mo. 
196 

319 
,5l=J  of  33  days. 

14  days. 

159  5 
15  9 

1,75,4  for  1  month. 

7 

14  d.  1  mo. 

12,27,8  for  7  months. 
87,7 

Ans. 

1.^,15,5 

13  doils.  15  cts.  5  ms. 

14.  What  is  the   discount  of  the  above  sum,  discounting 
for  60  days? 

Note.     As  notes  are  renewable  in  56  days,  the  interest  of 
all  securities  is  calculated  accordingly. 

66)210(3  discount  months.         319 

168  l,Oi==i  of  63  days. 

42  days.  3190 

159 


3,34,9  for  I  discount  m©. 
3 


10,m,7  for  3  do. 
28  d.  1  mo.  1,67,4 

14       I  83,7 


s 


12,55,3 
Ans.     1  i^  dolls.  55  cts.  8  ms. 

The   preceding  examples  shew  the  difference  betweea 
discounting  for  30  and  60  days. 


120  EQUATION  OF  PAYMENTS. 

What  is  the  discount  of  the  following   sums,  discounting 
for  30  days? 


dolls.      days. 

15. 

187  for    79 

16. 

219         115     - 

17. 

658           47 

18. 

2169         128     - 

dolls. 

cts. 

7ns. 

Ans.  2 

90 

0 

4 

94 

5 

6 

7 

4 

54 

b3 

2 

What  is  the  discount  of  the  following  sums,  discounting 
for  60  days  ? 

dolls,  cts.  7ns. 
Ans.  2     76     8 

4  72     2 

5  79     8 
^         -             52     5     4 

When  a  note  is  oifered  at  a  hank  for  discount,  two  endor- 
sers are  generally  required,  to  the  first  of  whom  it  is  said  to 
be  payable  :  I'hus,  A,  having  occasion  for  a  sum  of  money, 
procures  B  and  C  as  endorsers  to  his  note,  and  offers  it  for 
discount  in  the  following  form: 


dolls.        days. 

19. 

187  for    79 

20. 

219         115    - 

21. 

658           47 

22. 

2169         128    - 

100  Dollars. 


For  value  received.^  I  promise  to  pay  jB,  or  order^  at  the 

Bank^  on  demand^  one  hundred  dollars^  with  interest  after 

days.  A. 

When  state  notes,  bank  shares,  ^c.  are  lodged  in  a  bank 
as  security,  for  money,  a  nT)te  is  presented  in  this  form : 

For  value  received.^  I  promise  to  pay  the  President^  Directors 

and  Company  of  the Bank.,  or  their  order.,  at  said  Bank^ 

on  demand^ dollars.,  with  interest  after days. 

CD. 


EQUATION  OF  PAYMENTS. 

The  design  of  this  Rule  is  to  nnd  a  mean  t.me  for  the 
payment  of  several  sums  dire  at  ditierent  times, 

BuLR.  Multiply  each  sum  by  it-,  time,  ace*  divide  the  sum 
of  tl:(-  products  by  the  whole. debt ;  the  quotient  is  accounted 
the  mean  time. 


BARTER.  121 

EXAMPLES. 

1.  A  owes  B  200  dolls,  whereof  40  dolls,  is  to  be  paid  in 
3  months,  60  dolls,  in  5  months,  and  the  remainder  in  10 
months :  at  what  time  may  the  whole  be  paid  without  any 
injustice  to  either  ?         dolls.         mo. 

40  X        3=  120 

60  X        5=  300 

100   X      10=1000 


200  200)1420 

Ans.  7  mo.  and  3  days. 

2.  A  is  indebted  to  B  £120,  whereof  one  half  is  to  be  paid 
in  3  months,  one  quarter  in  6  months,  and  the  remainder  in 
9  months :  what  is  the  equated  time  for  the  payment  of  the 
whole  ?  Ans.  5  months  and  7J  days. 

3.  C  owes  D  1400  dolls,  to  be  paid  in  3  months;  but  I> 
being  in  want  of  money,  C  pays  him,  at  the  expiration  of  2 
months,  1000  dolls.:  how  much  longer  than  3  months  ought 
C,  in  equity,  to  defer  the  payment  of  the  rest  ? 

Ans.  2J  months. 
Those  who  are  exact  in  these  calculations  find  the  pre- 
sent worth  of  each  particular  sum,  then  find  on  what  time 
these  present  worths  will  be  increased  to  the  total  of  the 
particular  sums  payable  at  the  particular  times  to  come  ;  and 
Jthat  is  the  true  equated  time  for  the  payment  of  the  whole 


BARTER 

Is  the  exchanging  of  one  commodity  for  another  on  such 
terms  as  may  be  agreed  on. 

EXAMPLES. 

1.  How  many  quintals  of  fish,  at  2  dolls,  per  quintal,  will 
pay  for  140  hhds.  of  salt,  at  4  dolls.  70  cts.  per  hhd.  ? 
140 
4,70 

9800 
560 

dlls.       qtl  

If    2     :     1     ::     658,00  the  amount  of  the  salt* 

Ans.  329  quintals. 
M 


122  BARTER. 

2.  A  buys  of  B  4  hhds.  of  rum  containing  410  gallons,  at 
1  doll.  17  cts.  per  gallon  ;  and  253  lb.  of  coffee,  at  21  cts. 
per  lb.,  in  part  of  which  he  pays  21  dolls,  in  cash,  and  the 
balance  in  boards,  at  4  dolls,  per  thousand  :  how  many  feet 
of  boards  did  the  balance  require?         Ans.   127957i  feet. 

3.  B  has  C's  note  for  250  dolls,  with  6  months  interest  due 
on  it,  and  to  redeem  it  C  delivers  him  60  bushels  of  wheat 
at  Is.  (?d,  per  bushel,  50  bushels  of  corn  at  bs.  M,  per  bushel, 
and  the  balance  in  staves  at  30  dolls,  per  thousand  :  what 
number  of  staves  did  B  receive  ? 

Ans.  5550  staves,  or  4  m.  6  bun  and  10  casts, 

4.  B  bought  of  D  the  hull  of  a  schooner  of  70  tons,  at  16 
dolls,  per  ton,  and  paid  him  in  cash  500  dolls.  3  hhds.  of  mo- 
lasses containing  350  gallons,  at  64  cts.  and  is  to  pay  the  ba- 
lance in  New-England  rum  at  74  cts.  per  gallon :  how  many 
gallons  is  D  to  receive?  Ans.  535-5-  galls. 

5.  A  buys  of  B  250  quintals  offish,  at  25*.  per  quintal ;  in 
payment  B  takes  100  dolls,  in  cash,  2  hhds.  of  molasses  con- 
taining 87  and  92  galls,  at  3s  Sd.  per  gallon,  1  pipe  of  bran- 
dy containing  120  galls,  at  Is.  6d,  per  gallon,  and  gives  3 
months  credit  for  the  remainder :  required  the  balance  due, 
and  what  cash  would  pay  it,  allowing  the  interest  of  it  for 
the  time  at  6  per  cent,  per  annum,  as  discount  for  prompt 
payment  ? 

Ans.  Balance  is  682  dolls   27  cts.  6  ms.==672,04,2  in  cash. 

6.  C  sells  to  D  28,674  feet  of  boards  at  8  dolls.  50  cts.  per  . 
thousand,  and  takes  in  payment  i  cash,  4  barrels  N.  E.  rum 
containing  128  gallons  at  78  cts.  per  gallon,  1  barrel  of  sugar 
weighing  neat  2  cwt.  2  qrs.  4  lb.  at  10  dollars  per  cwt.  and 
the  balance  in  coffee  at  25  cts.  per  lb. :  how  much  money 
and  coffee  is  C  to  receive  ? 

Ans.  81  dolls.  24  cts.  3  ms.  and  149//„-  lb.  of  coffee. 

7.  C  has  nutmegs  worth  Is.  6c/.  per  lb.  in  ready  money, 
but  in  barter  he  will  have  8*. ;  D  has  tobacco  worth  9d.  per 
lb. :  how  much  must  he  rate  it  per  lb.  that  his  profit  may  be 
equal  to  C's?  Ans    9|J. 

8.  A  has  tea  which  he  barters  with  B  at  \0d.  per  lb.  more 
than  it  cost  him,  against  cambrick  which  stands  B  in  \0s.  per 
yard,  but  he  puts  it  at  12s.  6d. :  1  would  know  the  first  cost 
of  the  tea?  Ans.  35.  4c/.  per  lb. 

9.  A  has  240  bushels  of  rye,  which  cost  him  90  cts.  per 
bushel ;  this  he  barters  with  B  at  05  cts.  f c  r  wheal  that 
stands  B  in  99  cts.  per  bushel :  how  many  bushels  of  wheat 


LOSS  AND  GAIN.  irs 

is  he  to  receive  in  barter,  and  at  what  price  is  it  to  be  rated, 
that  their  gains  may  be  equal  ? 

Ans.  218/oV  bushels,  at  lO'U  cts.  per  bushel. 

10.  A  and  B  barter  some  goods;  A  puts  his  at  SO^e^  shil* 
lings,  and  gains  8  per  cent.  B  puts  his  at  24^^  shillings, 
and  gains  at  the  same  rate  :  what  was  the  first  cost  of  the 
goods?  Ans.  28^.  and  22s.  (jd. 

11.  A  and  B  barter;  A  has  cloth  that  cost  2Sd.  B's  cost 
him  22d.  and  he  puts  it  at  2bd, :  how  high  must  A  put  his  to 
obtain  10  per  cent,  more  than  B?  Ans.  35c?. 

^      12.  C  and  D  barter;  C  of  Is.  makes  65.  Qd.     D  of  7^.  6d. 
makes  Is.  Sd. :  who  has  lost  most,  and  by  how  much  per  cent.  ? 
Ans.  C  loses  1|  per  cent,  more  than  D. 


LOSS  AND  GAIN 

is  a  rule  that  discovers  what  is  gained, or  lost  in  buying  pr 
selling  goods,  and  instructs  merchants  and  traders  to  raise  or 
fall  the  price  of  their  goods  so  as  to  gain  or  lose  so  much 
per  cent.  &c. 

EXAMPLES. 

1.  Bought  a  piece  of  broadcloth,  containing  53  yards,   at 
4  dolls.  65  cts.  per  yard,  and  sold  at  5  dolls,  per  yard:  what 
is  the  profit  on  the  whole  ? 
dls.  cts. 
5 
4,65 

yd^      yds. 

If  I      :      ,35     :  :     53 
35 

266 
159 


1«,55     Ans.  18  dolls  55  cts. 

2.  If  1  lb.  of  coffee  cost  28  cts.  and  is  sold  for  31  cts.  what 
is  the  profit  on  3  bags,  weighing  293  lbs.  neat? 

Ana       Q    rlrklla      »70    r-fc 


lU  LOSS  AND  GAIN. 

3.  Bought  a  piece  of  baize  of  42  yds.  for  £4  14  6,  anS 
sold  it  at  2s.  6d.  per  yard :  what  is  the  gain  or  loss  on  the 
whole  piece?  Ans.  \0s,  6d.  gain. 

4.  A  merchant  bought  59  cwt.  3  qrs.  14  lbs.  of  iron,  at  112 
dolls,  per  ton,  paid  freight  and  charges,  24  dolls. :  what  is 
the  gain  or  loss,  if  he  sells  the  whole  at  37^.  4d.  per  cwt.  ? 

Ans.  13  dolls.  26  cts.  gain. 

5.  If  a  gallon  of  wine  cost  6^.  Sd,  and  is  sold  for  7*.  2d> 
what  is  the  gain  per  cent.  ? 

7     2 
6     8 

s.d,  £ 

If  6  8     :  6     :  :     100  Ans.  7^  per  cent.  gain. 

6.  When  20  per  cent,  loss  is  made  on  coffee,  sold  at  20 
cts.  per  lb.  what  was  the  first  cost  ?  Ans,  25  cts. 

7.  At  l^  cts.  profit  on  the  dollar,  how  much  is  it  per  cent.  ? 
Ans.   13|  per  cent,  or  13  dolls.  50  cts.  per  100  dolls. 

8.  A  trader  sells  his  goods  at  2^d.  profit  on  the  shilling, 
how  much  is  it  per  cent.  ?  Ans.  20f  or  £  20  16  8. 

9.  Which  is  the  better  bargain,  in  purchasing  fish,  17  shil- 
lings per  quintal,  and  4  months  credit,  or  16*.  8d,  cash? 

Ans.  They  are  alike. 

Proof.  The  present  worth  of  1 75.  found  by  discount,  is 
equal  to  I65.  8c^.  ;  and  I65.  8c?.  with  4  months  interest  will 
amount  to  17^. 

10.  A  bought  a  piece  of  shalloon,  containing  34  yards,  at 
35.  4d.  per  yard,  and  sold  it  at  12^  percent,  loss  :  how  much 
did  he  sell  it  per  yard  ?  Ans.  2^.  1  Id. 

11.  Bought  rum  at  90  cts.  per  gallon  :  at  what  rate  must 
it  be  sold  to  gain  20  per  cent  ?  Ans.  108  cents. 

12.  A  trader  bought  1  hhd.  of  rum,  of  a  certain  proof, 
containing  115  gallons,  at  1  doll.  10  cts.  per  gallon:  how 
many  gallons  of  water  must  he  put  into  it  to  gain  5  dollars, 
by  selling  it  at  1  dollar  per  gallon  ?  Ans.  16^  galls. 

13.  Bought  4  hhds.  of  rum,  containing  450  gallons,  at  1 
doll,  per  gallon,  and  sold  it  at  1  doll.  20  cts.  per  gallon,  and 
gave  3  months  credit :  now  allowing  the  leakage  of  the  rum 
while  in  my  possession  to  be  10  gallons,  1  would  know  the 
gain  or  loss,  discounting  for  the  present  worth  ot  the  debt  at 
6  per  cent,  per  annum  ?  Ans.  70  dolls.  19  cts.  gain. 


LOSS  AND  GAIN.  125 

14.  A  vintner  buys  59G  gallons  of  wine,  at  65.  3d.  per  gal- 
lon, in  ready  money,  and  sells  it  immediately  at  Qs.  9a.  per 
gallon,  payable  in  3  months  :  how  much  is  his  gain  or  loss, 
supposing  he  allows  the  interest  for  the  time,  at  6  per  cent, 
per  annum,  as  discount  for  present  payment  ? 

Ans.  £11   17  8  gained. 

15.  What  would  be  the  gain  or  loss  on  the  aforesaid  wine, 
supposing  the  discount  for  present  payment  to  be  made  at  2 
per  cent,  without  any  regard  to  time  i  Ans.  jtJlO  17  6  J  gain. 

16.  A  merchant  bought  a  parcel  of  cloth  at  the  rate  of  1 
dollar  for  every  2  yds.  of  which  he  sold  a  certain  quantity  at 
the  rate  of  3  dolls,  for  every  5  yds.  and  then  found  he  had 
gained  as  much  as  18  yds.  cost;  how  many  yards  did  he  sell? 

Ans.  90  yards. 

17.  Bought  rum  at  1  doll.  25  cts.  per  gallon,  which  not 
proving  so  good  as  I  expected,  I  am  content  to  lose  18  per 
cent,  by  it;  how  must  1  sell  itpergallon?  Ans.  1  doll.  2^  cts. 

18.  H  sells  a  quantity  of  corn  at  1  dollar  a  bushel,  and 
gains  20  per  cent. ;  some  time  after  he  sold  of  the  same,  to 
the  amount  of  37  dolls  50  cts.,  and  gained  50  per  cent. :  how 
many  bushels  were  there  in  the  last  parcel,  and  at  what  rate 
did  he  sell  it  per  bushel  ? 

Ans.  30  bushels  at  1  doll.  25  cts.  per  bushel  ? 

19.  A  distiller  is  about  purchasing  10,000  gallons  of  mo- 
lasses, which  he  can  have  at  48  cts.  per  gallon  in  ready 
money,  or  50  cents  with  2  months  credit :  it  is  required  t© 
know  which  is  more  advantageous  to  him,  either  to  buy  it 
on  credit,  or  to  borrow  the  money  at  8  per  cent,  per  annum 
to  pay  the  cash  price  ? 

Ans.  He  will  gain  136  dolls,  by  paying  the  cash. 

20.  A  tobacconist  buys  4  hogsheads  of  tobacco,  weighing 
38  cwt.  2  qrs.  8  lb.  gross,  tare  94  lb.  per  hhd.  at  9  dolls,  per 
cwt.  ready  money,  and  sells  it  at  I  \^iL  per  lb.  allowing  tare 
at  14  lb.  per  cwt.  to  receive  two  thirds  in  cash,  and  for  the 
remainder  a  note  at  90  days  credit:  his  gain  or  loss  is  re- 
quired, supposing  the  note  is  discounted  at  a  bank  where  dis- 

«count  is  made  for  60  days.    Ans.  283  dolls.  42  cts.  6  ms.  gain. 

M2 


126  ALLIGATION  MEDIAL. 

ALLIGATION  MEDIAL 


Is,  when  the  quantities  and  prices  of  several  things  are 
given,  to  find  the  mean  price  of  the  mixture  compounded  ot 
those  things. 

Rule.  As  the  sum  of  the  quantities  or  whole  composition 
is  to  their  total  value,  so  is  any  part  of  the  composition  to 
its  mean  price. 

EXAMPLES. 

1.  A  grocer  would  mix  ^5  lb.  of  raisins,  at  8  cts.  per  lb., 
and  35  lb.  at  10  els.  per  lb.,  with  40  ib.  at  12  cts.  per  lb.; 
w^hat  is  1  lb.  of  this  mixture  worth? 

lb.  cts.  cts. 

25  at  8  -  200 

35  -  10  -  350 

40  -  12  -  480 


100 

1030 

lb. 

cts. 

lb. 

100       : 

1030     : 
1 

:      1 

If 


1|00)10|30 

cts.  10^3         Ans.  10  cents  3  mills. 
8.  A   goldsmith  mixes  8  lb.  5i  oz.  of  gold,  of  14  carats 
line,  with  12  lb.  8^  oz.  of  18  carats  fine ;    what  is  the  fine- 
ness of  this  mixture?  Ans.   J6y\V  carats. 

3.  A  grocer  would  mix  12  cwt.  of  sugar,  at  10  dollfe  per 
cwt.  with  3  cwt.  at  8|  dolls,  per  cwt.  and  8  cwt.  at  7^  dolls, 
per  cwt. ;  what  will  5  cwt.  of  this  mixture  be  worth  ? 

Ans.  44  dolls.  78  cts.  2  ms. 

4.  A  refiner  melts  2j  lb.  of  gold,  of  20  carats  fine  with 
4  lb.  of  18  carats  fine  ;"'how  much  alloy  must  be  put  to  it  to 
make  it  22  carats  fine  ? 

Ans.  It  is  not  fine  enough  by  3^^  carats,  so  that 
no  alloy  must  be  put  to  it,  but  more  gold. 

5.  A  maltster  mingles  30  quarters  of  brown  malt,  at  28*. 
per  quarter,  with  46  quarters  of  pale,  at  30*.  per  quarter, 
and  24  quarters  of  high-dried  do.  at  255.  per  quarter: 
what  is  the  value  of  8  bushels  of  this  mixture  ? 

Ans.  £i  ds.  2^c/.|. 


ALLIGATION  ALTERNATE.  127 

6.  If  I  mix  27  bushels  of  wheat,  at  5^.  6d.  the  bushel,  with 
the  same  quantity  of  rye,  at  45.  per  bushel,  and  14  bushels 
of  barley,  at  ^s.  8d.  per  bushel ;  what  is  the  worth  of  a 
bushel  of  this  mixture  ?  Ans.  4^.  3|(/.ff. 

7.  A  grocer  mingled  3  cwt.  of  sugar,  at  565.  per  cwt.  G 
cwt.  at  £l  17  4  per  cwt.  and  3  cwt.  at  £3  14  8  per  cwt.  ? 
what  is  1  cwt.  of  this  mixture  worth?         Ans.  £2   11   4. 

8.  A  mealman  has  flour  of  several  sorts,  and  would  mix 
3  bushels  at  3*  bd.  per  bushel,  4  bushels  at  5*.  i)d.  per 
bushel,  and  5  bushels  at  4^.  Sd.  per  bushel;  what  is  the  worth 
of  a  bushel  of  this  mixture?  Ans.  4s\  Ijd.r^^. 

9.  A  vintner  mixes  20  gallons  of  Port,  at  5^.  4d.  per  gal- 
lon, with  12  gallons  of  White  wine,  at  55.  per  gallon,  30  gal- 
lons of  Lisbon,  at  Qs.  per  gallon,  and  20  gallons  of  Mountain, 
at  45.  iod,  per  gallon  ;  what  is  a  gallon  of  this  mixture  worth  ? 

Ans.  55.  3Jdf|. 

10.  A  farmer  mingled  20  bushels  of  wheat,  at  55.  per 
bushel,  and  3i^  bushels  of  rye,  at  35.  per  bushel,  with  40 
bushels  of  barley,  at  25.  per  bushel  ?  1  desire  to  know  the 
worth  of  a  bushel  of  this  mixture  ?  Ans.  35. 

11.  A  person  mixing  a  quantity  of  oats,  at  25.  Qd.  per 
bushel,  with  the  like  quantity  of  beans,  at  45.  Qd.  per  bushel, 
would  be  glad  to  know  the  value  of  1  bushel  of  that  mixture  ? 

Ans.  35.  6d. 

12.  A  refiner,  having  12  lb.  of  silver  bullion  of  6  oz.  tine, 
would  melt  it  with  8  lb»  of  7  oz.  fine,  and  10  lb.  of  8  oz.  fine  : 
required  the  fineness  of  1  lb.  of  that  mixture  ? 

Ans.  6  oz.  18  dwt.  16  grs. 

13.  If  with  40  bushels  of  corn,  at  45.  per  bushel,  there 
are  mixed  10  bushels,  at  Qs.  per  bushel,  30  bushels  at  55. 
per  bushel,  and  20  bushels,  at  3s.  per  bushel,  what  will  10 
bushels  of  that  mixture  be  worth?  Ans.  £2  3> 


ALLIGATION  ALTERNATE 

Is  the  method  of  finding  what  quantity  of  any  number  of 
simples,  whose  rates  are  given,  will  compose  a  mixture  oi  a 
given  rate:  so  that  it  is  the  reverse  of  Alligation  Medial, 
and  may  be  proved  by  it. 


128 


ALLIGATION  ALTERNATE. 


Rule.  1.  Write  the  rates  of  the  simples  in  a  column  un- 
der each  other. 

2.  Connect  or  link  with  a  continued  line  the  rate  of  each 
simple,  which  is  less  than  that  of  the  compound,  with  one, 
or  any  number,  of  those  that  are  greater  than  the  compound, 
and  each  greater  rate  with  one  or  any  number  of  the  less. 

3.  Write  the  difference  between  the  mixture  rate  and 
that  of  each  of  the  simples,  opposite  the  rates  with  which 
they  are  linked. 

4.  Then  if  only  one  difference  stand  against  any  rate,  it 
will  be  the  quantity  belonging  to  that  rate  ;  but  if  there  be 
several,  their  sum  will  be  the  quantity. 


EXAMPLES. 

1 .  A  merchant  would  mix  wines  at  14^.  19^.  1  bs.  and  225.  per 
gallon,  so  that  the  mixture  may  be  worth  185.  the  gallon: 
what  quantity  of  each  must  be  taken? 

at  145. 
at  165. 
at  195. 
at  225. 


6  at  145. 
1  at  165. 

7  at  195. 
4  at  225. 

Note.  Questions  in  this  rule  admit  of  a  great  variety  of 
answers,  according  to  the  manner  of  linking  them. 

t.  How  much  wine  at  65.  per  gallon,  and  at  45.  per  gal- 
lon, must  be  mixed  together,  that  the  composition  may  be 
worth  55.  per  gallon?       Ans.  1  qt.  or  I  gall,  of  each,  &c. 

.3.  How  much  corn,  at  25.  Gc?.,  35.  8c?.,  45.  and  4^.  Sd.  per 
bushel,  must  be  mixed  together  that  the  compound  may  be 
worth  35.  lOd.  per  bushel? 

Ans.  12  at  25.  6(i.,  12  at  35.  8d,^  18  at  45.,  and  18  at  45.  8c?. 

4.  A  goldsmith  has  gold  of  17,  18,  22  and  24  carats  fine^ 
how  much  must  he  take  of  each  to  make  it  21  carats  line  ? 
Ans.  3  of  17,  a  of  18,  3  of  22^  and  4  of  24. 


ALLIGATJON  ALTERNATE.  129 

5.  It  is  required  to  mix  brandy  at  8*.,  wine  at  7*.,  cider 
at  1^ ,  and  water,  together,  so  that  the  mixture  may  be 
worth  Iss.  per  gallon? 

Ans.  9  galls,  brandy,  9  of  wine,  6  of  cider,  and  5  of  water. 

When  the  xvhole  composition  is  limited  to  a  certain  quantity. 

Rule.  Find  an  answer  as  before  by  linking ;  then  say, 
As  the  sum  of  the  quantities,  or  differences,  thus  determined, 
is  to  the  given  quantity,  so  is  each  ingredient  found  by  link- 
ing to  the  required  quantity  of  each. 

EXAMPLES. 

6.  How  many  gallons  of  water  must  be  mixed  with  wine 
worth  3s.  per  gallon,  so  as  to  fill  a  vessel  of  100  gallons,  and 
that  a  gallon  may  be  afforded  at  2*.  ^d.  ? 

-Iso 


30 


(36 


36     :     100     ::     6  36  3G     :     100     ::     30 

6  30 


36)600(16  36)3000(83 

36  288 

240  120 

216  108 

24  12 

Ans.  83i  gallons  of  wine,  and  16|  of  water. 

7.  A  grocer  has  currants  at  4c?.,  6fl?.,  9d.  and  \]d.  per  lb. 
and  he  would  make  a  mixture  of  240  lb.  so  that  it  might  be 
afforded  at  8c^.  per  lb. :  how  much  of  each  sort  must  he 
take  ? 

Ans.  72  lb.  at  4d.^  24  at  6c?.,  48  at  9^.,  and  96  at  1  Id, 

8.  How  much  gold  of  15,  of  17,  of  18  and  of  22  carats  fine, 
must  be  mixed  together  to  form  a  composition  of  40  oz.  of 
20  carats  line  ? 

Ans.  5  oz.  of  15,  of  17  and  of  18,  and  25  oz.  of  22. 


1^0  POSITION. 

When  one  of  the  ingredients  is  limited  to  a  certain  quaiitity. 
Rule.     Take  the  difference  between  each  price  and  the 

mean  rate,  as  before  ;  then, 

As  the  difference  of  that  simple,  whose  quantity  is  given, 

is  to  the  rest  of  the  differences  severally,  so  is  the  quantity 

given  to  the  several  quantities  required. 

EXAMPLES. 

9.  How  much  wine,  at  55.,  at  5*.  6cf.,  and  at  6^.,  the  gallon, 
must  be  mixed  with  3  gallons,  at  45.  per  gallon,  so  that  the 
mixture  may  be  worth  55.  4d.  the  gallon  ? 

] ,  8  +  2=10 

)— [— U    I  8  +  2=10 

;_L.U     I  16+4=20 

>-_|-.^ /  16  +  4=20 

)     :      10     :  :     3        :     3 

10     :     20    ':  :     3        :     6 

10     :     20     :  :     3        :     6 
Ans.  3  gallons  at  55.,  6  at  55.  6d.^  and  6  at  65. 

10.  A  grocer  would  mix  teas  at  125.,  IO5.,  and  65.,  with 
20  lb.  at  45.  per  lb. :  how  much  of  each  sort  must  he  take  to 
make  the  composition  worth  85.  per  lb.  ? 

Ans.  20  lb.  at  45.,  10  lb.  at  65.,  10  lb.  at  IO5.,  and  20  lb.  at  125. 

11.  How  much  gold  of  15,  of  17,  and  of  22  carats  fine, 
must  be  mixed  with  S  oz.  of  18  carats  fine,  so  that  the  com- 
position may  be  20  carats  fine  ? 

Ans.  5  oz.  of  15  carats  fine,  5  oz.  of  17,  and  25  of  22. 


POSITION 

Is  a  rule  which,  by  false  or  supposed  numbers,  taken  at 
pleasure,  discovers  the  true  one  required.  It  is  divided  into 
two  parts ;  Single,  and  Double. 

sijYgle  position 

Is  by  using  one  supposed  number,  and  by  working  with  it 
as  the  true  one,  you  find  the  real  number  required,  by  the 
follow  mg 

Rule.  As  the  total  of  the  errors  is  to  the  given  sum,  so 
is  the  supposed  number  to  the  true  one  required. 


POSITION.  131 

Proof.  Add  the  sereral  parts  of  the  result  together,  and 
if  it  agrees  with  the  given  sum  it  is  right. 

EXAMPLES. 

1.  A  schoolmaster,  being  asked  how  many  scholars  he  had, 
said,  If  I  had  as  many,  half  as  many,  and  one  quarter  as  ma- 
ny more,  1  should  have  264  :  how  many  had  he  ? 

Suppose  he  had  72 

As  many     -       -  72 

I-  as  many  -       -  36 

}  as  many  -       -  18 

As     198     :     264     ::     72 

72 


Proof. 

528  96 

1848  96 

48 

24 

264 


198)19008(96  answer.                     24 
1782  


1188 
1188 

2.  A  person,  after  spending  i  and  J  of  his  money,  had  60 
<]ollars  left;  what  had  he  at  tirst?  Ans.   144  dolls. 

3.  A  certain  sum  of  monf^y  is  to  be  divided  between  4  per- 
sons, in  such  a  manner,  that  the  first  have  i  ot  it,  the  second 
J,  the  third  i,  and  the  fourth  the  remainder,  which  is  28  dol- 
lars ;  what  was  the  sum  ?  Ans.  1 1 2  doll?. 

4.  A  person  lent  his  friend  a  sum  of  money  unknown,  to 
receive  interest  for  the  same,  at  6  per  cent,  per  annum,  sim- 
ple inttM-est,  and  at  the  end  of  .^  years  he  received  for  prin- 
cipal and  interest  644  dollars  80  cents;  what  was  the  sum 
lent?  Ans.  496  dolls. 

DOUBLE  position- 
Is  by  making  use  of  two  supposed  numbers,  which,  if  both 
prov^  false,  are,  with  their  errors,  U'  he  thus  disposed  : 
Kli.e.     1.  Place  each  error  against  its  respective  position. 

2.  Multiply  them  crosswise. 

3.  If  the  errors  are  alike,  that  is,  bctiL  4r>:ater  or  i^oili  less 
ilian  the  given  number,  divide  the  diiierence  ol  the  products 


J52  POSITION. 

by  the  difference  of  the  errors,  and  the  quotient  is  the  an- 
swer ;  but  if  the  errors  be  unlike,  divide  the  sum  of  the  pro- 
ducts by  the  sum  of  the  errors,  and  the  quotient  will  be  the 
answer. 

EXAMPLES. 

1.  B  asked  C  how  much  his  horse  cost;  C  answered,  that 
if  he  cost  him  three  times  as  much  as  he  did,  and  15  dollars 
more,  he  would  stand  him  in  300  dollars  :  what  was  the  priqe 
of  the  horse  ? 

dolls.  dolls. 

Suppose  he  cost  90  Suppose  he  cost  96 

3  3 


220                                       288 

15                                         15 

285  too  little  by  15  dlls.     303  too  much  by  3- 

90         15— 

X 

96         3+ 

15     1440    270 

3       270 

3rs    18)   1710(95  answer. 

95 

162 

3 

90 

285 

90 

15 

300  proof. 

2.  Two  persons,  A  and  B,  have  both  the  same  mcome  ; 
A  saves  one-fifth  of  his  yearly  ;  but  B.  by  spending  150  dol- 
lars per  annum  more  than  A,  at  the  end  of  8  years  finds 
himself  400  dollars  in  debt ;  what  is  their  income,  and  what 
does  each  spend  per  annum  ? 

Ans.  Their  income  is  500  dollars  per  annum ;  also  A  spends 
400,  and  B  550  dollars  per  annum. 

3.  There  is  a  fis^h  whose  head  is  9  inches  long,  and  his 
tail  is  as  long  as  his  head  and  half  his  body,  and  his  body  is 
as  long  as  the  head  and  tail :  what  is  the  hole  length  of  the 
fish?  Ans.  6  feet. 


EXCHANGE.  135 

4.  Divide  15  into  two  such  parts,  so  that  when  the  greater 
is  multiplied  by  4,  and  the  less  by  16,  the  products  will  be 
equal.  Ans.    12  and  3. 

5.  A  man  had  two  silver  cups  of  unequal  weight,  having 
one  cover  to  both,  5  oz. ;  now  if  the  cover  is  put  on  the  less 
cup,  it  wiU  be  double  the  weight  of  the  greater  cup,  and 
put  on  the  greater  cup  it  will  be  three  times  as  heavy  as  the 
less  cup  :  what  is  the  weight  of  each  cup  ? 

Ans.  3  oz.  less,  4  oz.  greater. 

6.  A  person,  being  asked  in  the  afternoon  what  o'clock  it 
was,  answered,  that  the  time  past  from  noon  was  equal  to 
j\  of  the  time  to  midnight;  required  the  time. 

Ans.  36  miautes  pas^t  one. 


EXCHANGE 

Is  the  paying  of  money  in  one  place  or  country,  for  the 
like  vahie  to  be  received  in  another  place  or  country. 

There  are  two  kinds  of  money,  viz.  Real  and  Imaginary. 

Real  Money  is  a  piece  of  metal  coined  by  the  authority  of 
the  state,  and  current  at  a  certain  price,  by  virtue  of  the 
said  authority,  or  of  its  own  intrinsic  value. 

Imaginary  Aiuiiey  is  a  denomination  used  to  express  a  sum 
of  money  of  which  there  is  no  real  species,  as  vi  livre  in 
France,  a  pound  in  America,  because  there  is  no  specie  cur- 
rent, in  this  or  that  country,  precisely  the  value  of  either 
of  the  sums. 

Par  of  Exchange  is  the  intrinsic  value  of  the  money  of 
one  country  compared  with  that  of  another  country,  as  one 
pound  sterling  is  equal  to  thirty-tive  shillings  flemish. 

Course  of  Exchange  is  the  current  or  running  price  of  ex- 
change, which  is  sometimes  above  and  sometimes  belov*  par, 
varying  according  to  the  occurrences  of  trade,  or  demand  for 
money.  Of  this  course,  there  are  tables  pnblii^hed  daily  in 
commercial  cities:  thus  by  Lloyd's  List,  of  3d  December, 
1791.),  the  course  of  exchange  between  Hamburgh  and  Lon- 
don wari  32*.  6W  Flemish,  per  pound  sterling,  being  25.  5|^. 
under  par,  or  loss  to  London. 

N 


134  EXCHANGE. 

GREAT  BRIT  Am. 

The  money  of  account  is  Pounds^  Shillings^  Pence  and  Farthings. 

The  English  Guinea  is  21  shillings  sterling. 

Weights  and  meiuures  generally  as  in  the  United  States. 

The  United  States  Dollar  is  equal  to  4^.  6d.  sterling. 

To  change  Sterling  to  Federal  AJoney. 

Rule.  Annex  three  ciphers  to  the  sum  (if  pounds  only) 
and  multiply  it  by  4;  this  product  di\ide  by  9,  and  you  have 
the  answer  in  cents.  If  there  be  shillings,  kc.  the  usual  me- 
thod is  to  reduce  it  to  Massachusetts  money,  by  adding  one 
third  to  it,  and  then  reduce  this  sum  to  Federal. 

EXAMPLES. 

1.  Chanje  £48  Sterling  to  Federal. 
48000 
4 


9)192000 

21333^  cents.      Ans.  213  dolls.  33i-  cts. 
2.  Change  £389   17  4^  Sterling  to  Federal,  exch.mge  at 
331  per  cent,  that  is,    £133^  Massachusetts  for  £100  Ster- 
ling. 

1)389   17  4^  Sterling. 
129   19   U  Exchange. 


519   16  6    Massachusetts. 


,3)519,825 


cts.  173275  Federal.    Anc.  ^732  <^o]h  75  ctJ«. 
Note.     Sterling  is  changed  to  Massachusetts   nioj.ej  by  uddinp,  one 
third  lo  the  sum,  and  Massachusetts  to  Sterling  by  deducting  one  fourth 
from  it. 


To  change  I  eileral  Currency  to  Sterling. 
Rule.     Work  by  either  of  the  following  methods. 


EXCHANGE.  ISb 

EXAMPLKS. 

Change  1732  dollars  75  cts.  to  sterling. 

First  method.  Second  method. 

n32  1732,75 

,3 


4*.     J              346 
6/y.     1                43 
50  cents 
25  cents 

8 
6 
2 
1 

3 
H 

Ans.  389 

17 

^ 

5i9|825 
20 

lelooo 

12 


6|000 
1)519  16  6     Massachusetts. 
129   19   li  Exchange. 


Ans.  £389  17  4^  Sterling. 

2.  What  is  the  Federal  amount  of  an  invoice  of  goods, 
charged  at  £196   14  6  Sterling,  advancing  on  it  25  per  ct? 

25     i)  196   14  6     Sterling. 
49     3  7|  Advance. 
245   18   11 
Exchange  at  33i  per  ct.    81    19  4^ 

£327  17  6     Massachusetts. 
"3)327875 
cts.~T09291|     Ans.  1092  dls.  91|  cts. 

3.  The  Sterling  cost  of  certain  goods  being  £60  12  6, 
what  does  it  amount  to  in  Massachusetts  money,  advancing 
on  it  50  per  cent.?  60  12  6 

50  per  cent,  advance      30     6  3 


90  18  9 
Exchange  at  33^  per  cent,     30     6  3 


Ans.   121     5  0  Mnss.  money. 

The  mercantile  method,  with  50  per  cent,  advance,   is   to  double  the 
Sterling  for  Massachusetts  money,  thus  : 

60   12  0 

2 


£121     5  0  Massachusetts,  as  abore. 


136 


EXCHANGE. 


4.  An  invoice  of  good?,  charged  at  £52  19  7  sterling  is 
sold  at  75  per  cent,  advance  on  the  sterling  cost ;  how  much 
is  it  in  Massachusetts  money  ? 

62     19     7 
Advance  at  50         26       9     9^ 
25         13       4   10| 


92     14     31 
Exchange  at  33i  per  cent.  30     1 8     1 


Ans.  £123     12     4}  Mass.  money. 
The  mercantile  method  with  75  per  cent,  advance  is,  to  multiply  the 
sltrling  by  2l  for  Massachusetts  money. 
''  Thus,  52     19     7 


^t 

105 
17 

19     2 
13     2 

Ans.  £123     12     4j  Mass.  money ,^  as  above. 
6.  The  sterling  cost  of  certain  goods  b^ing  £214     11    6^ 
how  much  is  it  in  Federal  money,  advancing  thereon  65 
per  cent.?  214  11     6 

50     A     107     5     9    >  , 
10     }       21     9     1|^" 


advance. 


Exchange      i. 


343     6     4| 
114     8     91 


457  15     21  Massachusetts^. 
Or  thus,  214  11     6     Sterling. 

Exchansre     -i-       71    10     6 


286  2  0 
50  i  143  1  0 
10     I      28   12     2i 


457  15     2j-  Massachusetts. 


,3)457,759 
ilollars     15?5,86i     Ans.  15  dolls.  86 J  cts^ 


EXCHANGE.  137 

6.  What  is  the  amount  of  a  bill  of  exchange  of  £ll5  14  9 
sterling,  sold  in  Boston  at  1|  per  cent,  advance  ? 
1)115     14     9  Sterhng. 
38      11     7  Exchange. 

Massachusetts  money. 


154        6 

4  Mas 

^3)154,317 

514,39 

n 

Federal 

51439 
25719 

cents     771|53 

dolls,  els. 
Value  at  par  514  39 
Advance  7     71^ 


Amount  522     10^ 


dolls,    cts. 
Or  thus,     Value  at  par     514     39 


Advance  at  1  per  ct.     5     14     3 
'-      do.       2     57     1 


7     71     4    Adv.  at  li  per  cent. 


Amount    522     10     4 
7.  A  merchant  in  Boston  receives  a  parcel  of  goods  from 
London,  charged  in  the  invoice  at  the  following  prices,  and 
marks  them  for  sale  at  60  per  ct.  advance  on  the  sterling  cost; 
required  the  selling  price  of  each  in  Massachusetts  money. 
s.     d.  s.       d.  dlls.  c.  m 

13     8  ster.  adv.  60  per  ct.  29      U  Mass.  money,  or  4  85  3 

6  10         -         -         -  12     5i  -         -         -  2     7  3 

S4.--  7U  --  183 

6     li       -         -         -         13     04  -         -         -  2  17  6 

17  0         .  -         -         36     3i  •         -         -  6     4  6 
S3     1         -         .         .         70     6i           -         -         -           11   75  6 

1  2         -         -         -  2     5i  ...  41 

18  10         -         -         -         40     2  -         -         -  6  69  4 
11                -         -         -         23     5i           -         .         -            3  91 

2  4...  4  lU  ...  82  3 
32  3  -  -  -  63  9i  -  -  -  11  46  6 
27     9         .         -         -         59     2i           -         -         .           9  86  3 

>i  2 


138  exchange:. 

8.  A  watch,  that  cost  1 5  guineas  in  London,  was  sold  }» 
Boston  at  50  per  cent,  advance  on  the  sterling  cost;  what 
was  the  price  ? 

15  guineas=£l5  15  0  sterling. 


31    10  0  Massachusetts. 


,3)31,5 


Ans.   105  dollars. 
9.  How  much  is  the  premium  of  insuring  j£294  at  8  gui- 
neas per  cent.?  Ans.  j£24  13  11   sterling. 


MERCANTILE    METHODS    OF    CALCULATING,    vIz. 

*^i  2b  per  cent,  discount  from  the  sterling  cost^  multiply  it  by  I 
for  the  answer  in  Massachusetts  money. 

10 li 

par             ----_.  li 

12|  per  ct.  adv.  on  the  sterl.  cost,  multiply  it  by  l^. 

25             -----  1| 

31i     ....             -  1-1 

50              -             -              ...  2 

62^     -             -             -             -             -  Sli 

65             -             -              -             -             -  2| 

75       -             -             .             .             .  2i 

87i            -             -             •             -             -  2i 

100 2| 

125              ....             -  3 

"'    140       -             -             -             -             -  31 

450              .....  31 

1621 31 

175             .             -              -             -              -  3| 
200;       -              -              -              -              -4 


IRELAND. 

if  The  money  of  account  as  in  England,  but  different  in  va- 
lue.    The  par  between  England  and  Ireland  is  8i  per  cent, 
that  is,  iilOO  sterling  money  is  £j08  6  8  in  Ireland. 
Mercantile  weights  and  measures  the  same  as  in  England 
The  United  States  dollar  is  equal  to  4^^  \0\-d.  Irish. 
The  English  guinea  is  equal  to  22.^  9(/.  Irish. 


EXCHVNGE. 


139^ 


pence  in  a 
Or  reduce 
t,  and  Iheu  work 


To  r€(]tice  Irish  money  to  Federal. 
Rule.     Reduce  the  given  sum  to  half  pence,    annex  two 
ciphers  to  it,  ami  then  divide  by  1  17    (the  hall 
dollar)  and  the  quotient  is  the  answer  in  cents, 
the  Irish  to  Sterling,  by  deducting  Jg  from 
as  for  sterling. 

EXAMPLE. 

Change  j£278   15  9  Irish  money  to  Federal. 

First  method*  Second  method. 

i^78   i5  9  y'gj  27b    15     9  Irish. 

20  21     8   1 1  Lxchrtnge. 


5575 
12 

257     6    10  sterling. 
85   15     71 

66909 
2 

343     2     b\  Mass. 

,3)343,122 

1143,74  cents. 

9)13381800 

X  13=  117 

13)1486866 

114371  cents. 

Ans.  1143  dolls.  74  cts. 

To  change  Federal  money  to  Irish, 
Rule.     Multiply  the  given  sum  by  117,  reject  two  figure* 
from  the  product  to  the  right  hand,  and  the  remaining  figure* 
are  the  halfpence  in  the  given  sum. 
1.  Change  1143  dolls.  74  cts   to  Irish. 
114374 
117 


80061 a 

114374 
114374 

2)l3^8l7|5a 
12)66908 J 


2|';)557|5     8 


Ans.  £278   15     8f 


140  EXC|TANGK. 

If  the  Slim  is  dollars  only,  work  bj'  either  of  the  foUomo^ 
methofls.  -^v 

2.  Change  1537  dollars  to  Irish.  "h";  .. 

First  method.  Second  method* 

1537  at  4*.    lOirf.        1537 
3 


4..    \ 

307     8 

Sd.   i 

51      4 

8 

2       1 

12   16 

2 

i       i 

3     4 

^ 

461      2         Massachusetts, 
i  115     5     6  Exchange  at  25  per  ct. 


345   16     6  sterling. 
Ans.    £374  12  10^    ^3  28   16     4^  exc.  8J  p.ct.  or  Ic^.  on  l^. 

£374  12  \0X 
In  changing  Sterling  to  Irish  nioney  at  par,  ^^  is  added  to 
the  sum  for  Irish :  and  in  changing  Irish  to  sterJmg,  ^l  is 
deducted  for  sterling,  because  12  pence  English  are  equal 
to  13  pence  Irish,  making  the  exchange  Id.  in  a  shilling, 
1*.  '6d.  m  a  pound,  and  £8  6  8  per  cent. 

EXAMPLES. 

1.  Change  £394  17  6  sterling   to  Irish,  at  par,    or  £8^- 
per  cent. 

3?2)394     17     6 
32     18     U 


Ans.   £427      1.^     7J  Irish. 
2.  Change  £427      15     7j-  Irish  money,  to  sterling,  at  gj 
per  cent,  in  favour  of  England. 

yV)427/15     li 


32      18      1^ 


Ans.   £394      17     6  sterling. 
6    Change  £370  sterling  to  Iriih  at  d  per  cent. 
£  £  £ 

100     :      109     ::      370  Ans.  £403  6  0 

4.  Reduce  £403  6  Irish  money  to  Sterling,  at  9  per  ct. 
9 
100 

--  £    s. 

109     :     100    ::    403  6  Ans.  £370 


fe 


EXCHANGE.  141 


HAMBURGH. 

Accounts  are    kept  in  Hamburgh  in    Marks^  Shillings  Lubs^  or 
Stivers^  and  Dtniers. 

12  deniers,  or  2  grotes,  make  1  shilling  lubs,  or  gtiver. 
16  shillings  lubs^  stivers,  o'''  ^  i  u 

32  grotes     "         -         -         j 

Jilso^ 
12  grotes  or  pence  Flemish  make  1  shilling  Flemish, 
SO  shillings  Flemish       -         -         1  pound. 

Note,     3  marks         -  make  -  1  rix  dollar. 

Ik  do.       -         -         -         -  •  ]  pound  Flemish- 

A  shippound  in  Hamburgh  -  2S0  lb. 

A  ring  of  slaves      do.  -  240 

100  lb,  in  Hamburgh         -  -  1074  in  U.  States. 

100  ells  do.  -  -  62i  yards. 

The  currency  of  Hamburgh  is  inferior  to  the  bank  money  ; 
the  agio.^  or  rate,  is  variable;  Maj  14th,  1798,  it  was  20 
per  cent,  in  favour  of  the  bank. 

The  mark  banco  is  33^  cents.  (See  laws  of  the  U.  States.) 

EXAMPLES. 

1.  Change  12843  marks  to  Federal,  at  33^  cents  per  mark. 

33^=1)12843 

Ans.  4281  dollars. 

2.  In  4967  marks  8  stivers  banco,  how  many  dollars,  ex- 
change as  above  ? 

331=1)4967, 

1655,66| 
8  stivers         ,16| 


dolls.   1665,831 

Ans.  1655  dolls.  83i  ets. 


To  change  Hamburs^h  money  to  Sterling, 
Rule.     As  the  oiven  rat^  is  to  one  pound,  so  is  the  Havtt* 
burgh  sum  to  the  sieriiog  required. 


142  EXCHANGE. 

EXAMPLES. 

1.  Chang-e  9443  marks  9 J  stivers    to  Sterling,   exchange 
at  325.  6d.  Flemish  per  pound  Sterimg. 

s.     d.         £,  m.  St. 

32     6     :      1        ::       2443  9^ 

12  grotes.  32  2 


390  4886  19  grotes. 

7329 
19 

78195 


390)78 195(200£ 
780 

195 

20 


390)3900(105. 
3900 
Ans.  £200  10  0 

2.  In  12093  marks  12  stivers,  how  many  pounds  sterling, 
exchange  at  32^.  3rf.  Flemish  per  pound  sterling  ? 

Ans.  £1000 

3.  In    4178  marks  2  stivers,  hov^r  many  pounds  sterling, 
exchange  at  3U.  10^.  Flemish  per  pound  sterling? 

Ans.  £350 

4.  Change  1971  marks  13  stivers  to  sterling,  exchange  at 
355.  6d.  Flemish  per  pound  sterling.  Ans.  £148  2  4 


To  change  Sterling  to  Hamburgh  money, 

KuLE.     As  1  pound  sterling  is  to  the  given  rate,  so  is  the 
«tening  sum  to  the  Hamburgh  required. 


EXCHANGE.  143 

EXAMPLE. 

Change  £350  Sterling  to  Hamburgh  money,  exchange  at 
31*.  lOd.  Flemish  per  pound  Sterling. 
£         s.     d.  £ 

I     :     31    10     ::     350 
12 

382  grotes. 
350 


19100 
1146 


2)133700  grotes. 
16)6t)859  Slivers. 


4178  2  Ans.  4178  marks,  2  stivers. 

Proving  the  answers  in  the  preceding  case  will  further  exemplify  this. 


To  reduce  Current  to  Bank  money. 

Rule.     As  100  marks  with  the  agio  added  is  to  100  hank, 
30  is  the  current  money  to  the  bank  required. 

EXAMPLES. 

1.  Change  560  marks  8  stivers  current  to  banco,  agio  at 
18  per  cent. 

18 
100 

118  :   100  ::  560  8.  Ans.  475  marks. 

2.  Change    2366  marks  current  to  banco,   agio  at  tO  per 
cent.  Ans.    1971  mark;-,  !0|  stivers. 

3.  Change  7456  current  marks  to  banco,  agio  at  -'Z'-Z  per 
cent.  Ans.  6111  marks,  7  slivers. 


144  ^  EXCHANGE. 

To  change  Bank  to  Current  Money, 

Rule.     As  100  marks  i«  to  100  with  the  agio  added,  so  is 
the  bank  given  to  the  current  reuuired. 

EXAMPLES. 

1.  Change  475  marks  banco  to  current,  agio  at  18  per  ct, 
18 


m. m. 

100  :  118  :: 475 

Ans.  560  marks,  8  stivers. 

Or  thus,  475 

18 

475       bank. 



85  8  agio. 

3800 

.— . — 

475 

560  8  as  above. 

85150 

16 

8100 

2.  Change  1971  marks,  10|  stivers  banco  to  current,  agio 

at  'iO  per  cent. 

m. 

9, 

20  J) 1971 

10|  banco. 

3^J4 

51-  agio. 

Ans.     23{j6 

0     current. 

PRACTICAL  qUESTIOjYS, 

1.  How  much  will  63452  lb.  of  cotton  come  to  at  8  grote« 
per  lb.  ? 

ib.         gr.  lb. 

1:8:;     63452 
8 


2)507610  grotes. 


16)253808  stivers. 


Ans.       15b 6 3  marks. 


EXCHANGE.  145 

g.  What  will  361  lb.  of  cotton  come  to  at  bOd.  per  lb.  ? 
Note.     cL  is  the  mark  for  pence  Flemish,  equal  in  value  to  half  sti- 
vers or  half  shillings  lubs. 

lb,         d,  lb, 

1      :     50     :  :     351 
50 


2)17550  grotes,  or  pence  Flemish. 

16)8775  stivers. 

548  7         Ans.  548  marks  7  stivers. 
S.  What  will  339  bars  Russian  iron  come  to,  wt.  19662  lb. 
at  35^  marks  per  shippound  ? 


lb.              m.                    lb. 

280     :       351     :  :     19662              Ans.  2492  m. 

I4stiv 

m. 

St. 

4. 

280  lb.  of  conon       -       at 

21  grotes  per  lb. 

- 

183 

12 

6. 

40024  lb.  coffee 

Si  stivers 

- 

2063 

10 

€. 

2438  pipe  staves 

16  marks  per  ring 

of  240     162 

9 

7. 

3540  hhd.  do. 

8h  do.            do. 

- 

125 

6 

8. 

529  barrel  do. 

54  do.            do. 

. 

11 

9 

9 

1 790  ib.  sugar 

214  pence  per  lb. 

- 

IISS 

10 

10. 

4892  lb.  rice 

184  m:irks  per  100 

- 

892 

12 

11. 

4  pieces  ;0-4  bedtick 

24     do.         do. 

- 

96 

0 

12. 

140  half  pint  tumblers 

8     do.  per  100 

. 

11 

3 

13. 

100  boxes  window  glass 

23     do.  per  box 

. 

^300 

14. 

1526i  lb.  coffee 

IQh  stivers  per  lb. 

- 

1574 

S 

15. 

245  bars  iro-i,  wt.  8434  lb. 

4 1  nKirks  per  shippound 

1235 

16. 

10  bales  hemp,  wt.  14' OS  lb. 

74    do.             do. 

3728 

17.  What  is  the  commis^iun  on   18270  marks,  at  2^  per    || 
cent.?  Ans.  456  m.  I2"st, 

18.  VVhat  is  the  interest  of  6370  marks,  for  3  months,  at 
5  per  ct.  per  annum?  Ans.  Id  m.  10  st, 

O 


146  EXCHANGE. 

19.  Change  5955  marks  7^  stivers  to  Dutch  Florins,  at 
38i  grotes  per  florin. 

m.  St. 

5955      71 
grotes  in  a  niark=32      2  grotes  a  stiver. 

1 1  910     15  grotes  in  7 J  stivers. 
17865 

15^ 

grotes  381     190575  grotes. 
.2  2 

77"  )  381750  (  4950  gilders. 
308 
731 
693 


385 
385 
— ^-  Ans.  4950  gild,  or  flop. 

20.  An  American  merchant  orders  his  correspondent  in 
Amsterdam  to  remit  4980  florins   16^,  stivers  to  Hamburgh; 
this   heing  done    when  the    exchange  is  r^9i    stivers  lor  2 
marks,  vsrhat  sum  is  he  credited  for  in  Hamburgh  ? 
St.  m.  Jl.         St. 

391     :     2     ::     4980      lUj 
4  20 


157  99616^ 


199233 
4 


157)79^932(5076  marks. 
785 

1193 

1099 

942 
942 
Ans.  5076  marks. 


EXCHANGE.  147 

HOLLAND, 

Accounts  are  kept  in  Florins  or   Gilders^  Stivers^  Dcniers  or 
Pennings, 

8  penning"?  -  make         -         1   grote. 

2  grotet,  or  16  pennings      -         -         -     1   sliver. 
20  stivers,  or  40  grotes    -         -         -  1  gilder  or  florin. 

Also, 
12  grotes  or  6  stivers         -         -         -         i   shilling. 
20  shillings,  or  6  gilders        -         -         -     1   pound  Flemish^ 
2k  dorms         -         -         -         -         -  1   rix  dollar. 

The  florin  or  gilder  of  the  United  Netherlands  is  estima- 
ted m  the  United  States  at  40  cents,  or  2  cents  per  stiver. 
100  Ih.  in  Amsterdam  make  109|  in  the  United  States. 
100  ells         do.  75    yards  do. 

la  liquid  measure,  16  mingles  make  1  steckan. 
8  steckans     -       1  aum. 

EXAMPLES. 

1.  Change  1954  florins  to  Federal  money  at  40  cts.  per  floria. 
1954 
40 


dolls.  78  1,(50  Ans.  781  dolls.  60  cts. 

£.  Change  2653  gilders  17  stivers  to  Federal  money,  at 
40  cents  per  gilder. 

2653     17  Or  thus:  2653      17 

40      2  20 


106120     34  53077  stivers. 

34  2  cents  per  stiver. 


106154  cents.  1061,54 

Ans.    1061  dolls.  54  cent j», 
3.  Change  1061  dolls.  54  cts.  to  gilders,  at  40  cts.  per  gilder. 
2)106154  cents. 

2|0)5'^0717  stivers. 

2653     17  Ans.  2653  gild.  17  stiv. 


148  EXCHANGE. 

3.  What  must  be  paid  in  Boston  for  an  invoice  of  goods 
charged  at  691  florins  17  stivers  ;  allowing  the  exchange  at 
40  cents  per  florin,  or  2  cents  per  stiver,  and  advancing  or 
it  60  per  cent.? 


591      17 

20 

dolls. 

cts. 

1  IQdl  stivers. 

am.  of  invoke 

236 

74 

2 

advance 

142 

04 

dolls.  236,74 

Ans. 

378 

7» 

60  per  cent. 

142,0440 

To  change  Sterling  to  Flemish. 
Rule.     As  1  pound  sterling  is  to  the  given  rate,  so  is  the 
sterling  given  to  the  Flemish  required. 

EXAMPLE. 

1.  In  £100  10^.  sterling,  how  many  gilders,  exchange  ai 
33*.  Od.  Flemish  per  pound  sterling? 
£,         9.     d.  £,      s. 

1     !    33     9     ::     100     10 
20         12  20 

20      405  grts.       2010 
403 


10050 
80400 


f|0)8 1405,0 

2)40702|  grotei. 
^j0)2035|li  stivers. 

1017  11 J         Ans.  1017  gild,  llj  stir. 


To  change  Flemish  to  Sterling. 
Rule.  As  the  given  rate  is  to  £l  sterling,  so  is  the  Flent- 
i$h  given  to  the  sterling  required. 


EXCHANGE.  149 

EXAMPLE. 

Ghani^f*  1017  gildors  11  J-  stivers  to  sterling,  exchange  at 
335.  9ii.  Flemish  per  pound  sterling. 
s.     d,         £  fl.         St. 

33     9     :      1      ::      1017      111 
12  40        2 


405  grotes.  4U680     221 

221 

405)40702^(100 
405 


2U2J 
20 


405)1050(10 

4050  Ans.  £100   1# 


To  change  Current  money  to  Bank. 
Rule.      As  100  gilders  with  the  agio  added  is  to  100  bank, 
so  is  the  current  money  given  to  the  bank  required. 

EXAMPLE. 

Change  023  gilders  9i  stivers  current  money  into  bank, 
agio  at  4^  per  cent. 

S'  g'  g'       ^• 

I04i      :      100     :  :     823     9J 
20  20 


2090  164691 

100 


2090)164^920(788  gilders. 

To  change  Bank  money  into  Current. 
Rule.    As  100  gilders  bank  is  to  loo  with  the  agio  added^ 
tso  IS  the  bank  mouey  given  to  the  current  required. 
example. 
Change  788   gilders    bank  money  to  current,    agio  at  4^ 
per  cent. 

g.  g.  g. 

100     :     lu4i     ::     liS3       Ans.  023  gilders,  9]  stir. 
0  2 


I5(i  EXCHANGE. 

PRACTICAL  qUESTIOJVS, 

I.  What  will  18f'.7  lb.  oi  coffee  come  to  at  19  stivers  per  lb.? 
1867 
19 


16803 
1867 


210)3547|3  stivers. 

1773  13  Ans.   1773  gilders  13  stivers; 

2.  What  will  9*2  hhds.  of  sugfar  come  to,  wcig-hmg  UM242 
lb.  gross,  deducting  2  per  cent,  for  good  weight,  tare  18  pei* 
cent,  at  21  grotes  per  Ih.  ? 

104242 
deduct  2  per  cent.  2085 

102157 
rare  18  per  cent.  18388 

83769  neat  wt. 
21 


83769 
167638 


8)1769149  grotes* 

2|0)87957|4i  stivers. 

43978  14i  Ans.  4397S  gilders,  14^  stiven> 

3.  What  will  251    bars  of  iron  come  to,    weighing  groSi^ 
10364  lb.  at  9f  gilders  per  lb.  deducting  2  percent.? 
10364 
91 


93276 

6182 
2691 

g- 
2percent.=:J^)10iO 

8 

9 
4 

12 
8 

1010,49 
20 

Ans.  990 

6 

-0 

9,80 
16 

i2,8d 


EXCHANGE. 


151 


4.  What  will  4  43  steckans  2  miogles  of  brandy  come  to  at 
42  giidei*s  per  ap.ni  ? 
8)M3 


17     7 

a 

42 

34 

68 

4  steckans  h 

21 

2       do.        k 

10  10 

1       do.       h 

5     5 

2  mingles    X 

0  13 

2 

d. 

2^315  1b.  of  sugar 

6. 

565<j0 

7. 

27093 

8. 

8189  lb.  of  coffee 

9. 

4650 

10. 

1970 

11. 

39285 

12 

213  ells  linen,  208  payable 

13. 

4190  lb.  butter 

- 

14. 

6476 

- 

15. 

20 : 2  lb.  lead 

- 

16. 

214  steck.  11  ming. 

.  brandy 

751     8     2         Ans.  761  gild,  8  stiv. 


23  grotes  per  lb. 

23         -         -         . 

25h       -         '         - 

234  stivers 

234 

191 

2)4        - 

30         -         -         - 

13  gild,  per  40  lb. 

in      -       -       - 

13i  do.  per  100  lb. 
42  do.  per  aum 


2  pennings, 
gild.  st» 
12256     2 
35350 
17271   li 
9622     1 
5405  12 
1945     7 
41740     6 
312 
1361   IS 
1861    17 
271   12 
1127     2 


DENMARK. 

Accounts  art  kept  in  Danish  Current  Dollars    and  Shillings^ 
reckoning  9b  skittings  to  the  dollar. 
Thfi  course  of  exchange   on  London  in  September,   1799, 
was  5  rix  or  Danish  dollars  for  I  pound  sterling. 

The  rix  dollar  of  Denmark  is  estimated  at  100  cents — {See 
Laws  of  the  United  States  ) 

96  pounds  of  Denmark  make  100  pounds  of  the  U.  States. 
Their  weights  are  shippounds,  lispounds^  and  pounds, 
16  pounds         -         make         -  1  lispound. 

20  iispounds,  or  320  pounds      -  1  shlppound. 

EXAMPLES. 

1.  How  much  will  8  pieces  of  platillas  come  to  at  9  dolls. 
56  skiliings  per  piece  ? 
9     66 
8 


76  64 


Ans.  76  dolls.  64  skilk. 


152  EXCHANGE. 

2.  How  much  will  1418  bars  of  iron  come  to,  wei<i'hino; 
263  shippouuds  9  lispounds  aad  4  pounds,  at  15  dolls,  per 
shippound. 


lb.        d.         s.    lis.lb. 
32j  :   15  ::  263  9  4 
20 

5269 
16 

31618 
5269 

Or              ship. 
263 
15 

lis.             3945 
5^3 

4  i          3 

5  lb.   ,V         0 

72 
<>0 
18 

Ans.  3951 

9d 

84308 
15 

32l0)126462lu(3951 
96 

304 


166 
160 

62 

32 

'  30 
96 

32)2880(90 

2880  Ann.  3951  dolls.  90  skills. 

3.  Whnt  is  the  commission  on  21545  Danish  dolis.  13  skil- 
lin^y,  at  2  per  cent.  ?       21545    13 

2 


43o,9n  26 
96 


566 
810 


r^C^,6^         Ans.  450  dolls.  86  skills. 


dls.  sks. 

dls.  sks. 

3  80 

- 

15  32 

9  5t> 

- 

4713   16 

17  G4 

. 

229  64 

12 

- 

288  08 

15 

- 

750  00 

SOpVshi 

W 

'dl884    18 

3G 

9000  00 

11 

5074     3 

EXCHANGE.  158 

4.  What  will  4  hhds.  of  snp^ar  come  to,   weighing  gross 
4314  lbs.  tare  17  per  cent,  at  22  skilling^s  per  lb.  ? 

An8.  820  dolls.  62  skills. 


8.       4  pieces  table  cloth 
6.     50     do.  -         -         - 

7      13     do.  ... 

8.  24     do.  -         -         - 

9.  50     do. 

10.  100  coils  cord,  wt.  62sk.  16/.  2/6. 

11.  85  bund.  cl.  hemp,  250 

12.  1951  bars  Kus.  iron,  362  8   10 

13.  How  many  Danish  dollars  will  be  received  in  Copen- 
hagen for  a  bill  of  £2300  on  London,  exchange  at  5  rix  dol- 
lars per  pound  sterling  t  Ans.   1 1500  dolls. 

14.  A  bill  is  drawn  in  Copenhagen  for  18574  marks  7 
stivers,  Hamburgh  money,  when  the  exchange  is  128  Danish 
dollars  for  100  rix  dollars  in  Hamburgh:  how  many  Danish 
dollaus  does  it  amount  to  ? 

Note.     Three  marks  are  equal  to  I  rix  dollar. 

m,        r.d.  m.         st.  r.d.      sk. 

If3     :      1     ::      18574     7     :     6191     46 

r.d,  D.d.  r.d.       sk. 

If  100     :      128     ::     6191      46         Ans.  7925    D.dolls.  6  sjc. 
Or  thus,     3)18574     7     Hamburgh  mone^'. 

6191   46 
t8  per  cent.     1733  56 


7925     6     Danish  money,  as  above. 


BREMEK 


Accounts  art  kept    in  Rix  Dollars    and  Gr'otes^    reckoning  72 
grotes  to  the  rix  dollar^  which  is  equal  to  2-\  marks. 

On  the  29th  November,  1795,  the  exchange  on  LondoQ 
was  551  rix  dollars  for  £iOO  sterling. 

In  1^02,  the  course  of  exchange  on  the  United  States  was 
75  cents  per  nx  dollar. 

'1  he  BremiMi  last  is  equal  to  80  bushels  in  the  U.  States. 

lUO  ib.  m  Bremen  are  ecjual  to  110  lb.  m  the  U.  States. 


154  EXCHANGE. 

EXAMPLES. 

\.  What   will  1104  lb.  of  coffee  come  to,   at  32 J   grotes 
per  lb.  ? 

1104 
S2| 

2208 
33  2 
552 
276 

r.d.  groteSi 

72)36156(602     12 
360 

156 
144 

12  Ans.  602  rix  dollars  12  grotes; 

2.  What  is  the  commission  on  7621  nx  doils.  6  gr    at  3J 
per  cent.  ?  Ans.  26fci  nx  doils.  53  grotes. 

r.  dUs.  gr, 

3.  3071  lb.  coffee  at  32 J  grotes  per  lb.     -     1396     63 
4        400  -  3^f  -         -  .       181      18 

5.  706     -     33^    .    .     -   328  35 

6.  31407  lb.  sugar   15|    *    -    -  6870  20 


AKTWERP. 

Accounts  are  kepi  in  Antwerp  in  Gilders^  Shillings  and  Grotis. 

12  grotes         -  make  -         -  1  shilling. 

3^  shiHm<2:s,  or  40  grotes,  -         -       1  gilder. 

The  Braband  or  Antwerp  grotes  are  of  the  value  of  the  cents  of  the 
Unifed  States,  a  j^ilder  being  reckoned  al  40  cents.  In  the  current  mo- 
ney of  Aniweip  they  have  stivers  of  the  value  of  the  stiver  of  Amster- 
dam, or  2  cents  Uniied  States  currency. 

100  pots  binband     =     36^  gallons  United  States. 
96  lb.  AnUverp       =      100  lb.  do. 

100  Brabiuid  ells,  about    74  yards  American. 
The  new  quintal  of  Antwerp  consists  of  10  mjriagramme* 
dr  204  lb.  14  oz.   ^voirdupois  weight. 

The  loss  on  Sugar  ex(>orted  from   America  to   Antwerp  if 
22|  per  cent,  viz   tare  14  lb.  per  100  lb. — good  weight  2  lb. 
—loss  of  weight  5  lb. — discount  1|  lb.   equal  to  221  lb.  per 
lOu  lb. 
Loss  on  Cotton  12J-  per  ct, — on  coffee  in  bags  ll-J-  per  ct. 


EXCHANGE.  155 

EXAMPLES. 

1.  A  cargo  consisting  of  48  hhds.  sugar,  weighing  376 
cwt.  1  qr,  14  lb.  valued  per  invoice  al  12  dolls,  per  cvvt. 
and  6b  bags  coffee  weighing  7.345  lb.  at  32  cents  per  lb.  is 
sold  in  Antwerp;  what  sum  wat?^  received  for  it  in  gilderg 
and  grote^,  at  40  cents  per  gdder,  allowing  the  customary 
deductions  for  tare,  ^c.  at  an  advance  of  33^  per  cent,  from 
the  Invoice  ? 

cwt.  qrs.  lb.  lb, 

37t)    1    14  7345 

Tare,  &c.  22J  per  ct.    84  2  20^    Tare  SiC.  Ill  p.  ct.  844 1 

NeatSyi   2  21^  Neat     65004^ 
32 


dolls,  cts.  13000 

12  00  19500 

10  16 


120 

00 

10 

1200 

00 

2 

dolls.  2080,16 


2400  00  value  of  200  cwt. 


80  00 

. 

90 

12  00 

• 

1 

6  09 

- 

2  qr<5. 

1  50 

. 

14  lb. 

75 

«. 

7 

5 

3 

^ 

^ 

Value  of  suirar     3500  40  3             291   2  2!^ 
do.  coffee     2080   H".  0 ■ 


Adv.  331=1-  ineo  18  7 


5530  56  3  4|0)74107j5  cent« 


18601  35 


dolla.  7440  75  0 

Ans.  18601  gilders  35  grains. 


J  66  EXCHANGE. 

2.  What  sum   mupt  be  paid    in  Boston   for  an   invoice  of 
goods   imported    from  Antwerp,  amonntins^  to  7315  gilders, 
exchange  40  cents  per  gilder,  at  an  advance  of  40  percent.? 
7315  731F, 

40  per  ct.  advance.     2926  advance. 

2926,00  10241 

40  cts  per  gilder. 


Ans.  409e  dolls.  40  cts. 


RUSSM. 

Jiccowits  are  kept  in  Petersburgh  in  Rubles  and  Copets^  reckon- 
ing 100  copecs  to  1  ruble. 

The  course  of  exchange  on  London,    in  July,    1796,  was 
34|c/.  sterling  per  ru'tle. 

Ditto  on  Amsterdam,  30  stivers  banco  per  ruble. 
Ditto  on  Hamburgh,  Aug.  1798,  2^'!  «5tivers  banco  do. 
Ditto  on  United  States,  Sept.  1802,^55  cents  do. 

100  lb.  Petersburgh    weight   are  equal   to  883  lb.   in  the 
United  States. 

Their  weights  are  Barquits,  Poods,  Pounds,  &  Zollotnicke. 
96  zollotnicks         -         make         -  1    pound. 

40  pounds      -----  1    pood. 

10  poods 1   barquit. 

Their  long  measure  is  the  arsheen,  of  28  American  inch- 
es: 9  arbheens  are  equal  to  7  ^'anls. 

EXAMPLES. 

1.  What    will  7500  arsheens   of  ravens  duck  come   to  at 
14i  rubles  for  50  arsheens? 
arsh,         rvb.  ar^h. 

50     :     14V     ::     7500  Ans.  2175  rubles. 


EXCHANGE.  157 

2.  What  will    813  poods  5  lb.  of  clean  hemp   come  to  at 
30^  rubles  per  barqait? 

ib.  rub.  p.  lb. 

400  :  30^   : :  813  5 
40 


32525 
30| 

975750 
16262 


4|00)9920il2 

2480,03     Ans,  2486  rubles  8  copecs,* 
3.  What  Will  284S  poods  5  lb.  ot  bar  iron  co^ie  to  at  200 
copecs  per  pood  ?  2846 

200 


569200 
5  lb.     I  25 

copecs      569225  Ans.  5692  rubles  25  copecs. 

4.  What  is  the  commission  on  bzbo  rubies  dd  copecs,  at 
3  per  cent.'/  5266,33 

3 


157,68,99    Ans.  157  rubles  68  copocs. 

rub.  cop. 

5.  4997i  arsheens  flems  24  rubles  per  50  arsheens     2393     SO 

6.  1700         do.       drillings     34  copecs  per  arsheen  578 
7         355         do.       ticking    100     do.                do.                   355 

8.  U8|       do.  do.        110     do.  do.  180     62 

9.  200  pieces  of  sail  cloth    21  rubles  per  piece  4200 

10.      2 1. 0 i  poods  25  lb.  hemp    31    do.     per  barquit  65.5     04 

11.  ;;0.v  ill  iiiy  rubles  uiust  be  r- ceiveJ  iii  Petersinirgh, 
for  a  bill  orio*)OU  fi^ilders  on  Amsterdam,  when  the  exchange 
is  30  slivers  per  ruble? 

St.  cop.  gild.  gild. 

A«30     :      100     ::      15500  Or  thus,  i)l"6500 

20  5166,6G| 


310000  stiyers.                    10333,331^ 
100  -. 


3l'>)3l0u(>o(;|0 


10333,331        Ans.  10333  rub.  33^  cop. 
P 


158  EXCHANGE. 

12.  A   bill  of  £3000    sterling    is  drawn  on  London,    ex- 
change al  31|c/.  sterling  per  ruble:  what  is  its  value  in  Fe- 
te rsburgh  ? 

d,       rub,         £. 

As  31J    :  1    :  :   3000 

4  20 


127  60000 

12 


720000 
4 


127)28auOOO(22677  rubles. 
254 

340 
254 


860 

762 

980 

889 

910 

889 


127)2100(16  copecs. 

127 

830 

762 


68       Ans.  22677  rub.  16  cop^ 
Two   cipbor««   are  annexed    to  the  remainder   instead  of 
(ftiultiplying  by  100  copecs. 


FRAACE, 

12  deniers  =  1  sol,  20  sols  =  1  lirre. 

The  crown  of  exchange  is  3  livres  tournois. 

A  livre  tournois  of  France  is  estimated  at  18 J  cents  in  the 
IJnit^d  States. 

NOTE,  The  word  tournois,  is  applied  to  the  money  of  France,  as 
sterling  i»  to  the  money  of  Engkad. 


EXrHANGE.  15§ 

1.  Chani^e  £1220  sterling  to  French  money,  exchange  at 
17|<i.  per  crown  of  3  livres  tournois.  ^ 

d.         liv.         £ 
11 f     :    3  ::    \t20 
8  20 

141  24400 

12 

292800 


2342400 
3 

141)7027200(49838  livres. 
564 

1387 

12t)9 


1182 
1128 

540 
423 

1170 
1123 

42 
40 

141)840(55. 
705 

135 
12 

141)1620(11(1. 
141 

210 
141 


69     Ans.  49838  llv.  6  sols,  11  den. 


100  EXCHANGE. 

2.  Change  £400  sterling  to  French  money,   exchange  at 
17|c?.  sterling  per  crown  of  Slivres. 

Ans.   16  225  Hv.    Is.  O^d. 

3.  Change  4224  livres  tournoia  to  sterling,  exchange  at 
Hid.  per  crown  of  3  livres. 

Hv.         d.             Hv. 
3     :     17}    :;    4224 
[H 

29568 

4224 
21  i2 

3)73920 

12)24640 


2l0)205p  4 


102  13  4  Ans.  £102  13  4. 

Or,  fake  ^  of  the  given  sum  to  reduce  it  to  crowns,  and 
multiply  by  the  rate  of  exchange;  the  product  will  be  th^ 
ai»sw«r  in  pence. 

4)4224  livres.  . 

1408  crowns. 


9856 
1408 
704 

12)24640  pence. 


2|0)205|3  4 


£102  13  4  as  above. 

4.  Change  49838  livres  5*.  ll|-f(i.  to  sterling,  exchange 
lit  ll^d.  sterling  per  crown.  Ans.   £l220 

5.  What  will  2434  velts  of  brandy  come  to  at  320  livrei 
per  29  velt«?  Ans.  2t>857  Hv.  18*.  Id. 


EXCHANGE.  IGl 

G.  What  is  the  freight  of  3302^  veils,  at  9  livres  per  ton^ 
of  1«0  veits  ?  Ans.  241liv.  13^   9d. 

7.   VVhat  is  the  commission  on  36591  liv.  2  sols,  4  den.  at 
2^  percent.?  Ans.  914  liv    lbs.  6  den. 

'8.   What  is  the  interest  of  66476  liv.  \0s.  9  den,  for  one 
month  and  10  days,  at  \  per  cent,  per  month? 
A)b6476   10     9 

332|38     5     4 
20 


7165 
12 


7|84 

332     7     7 
10  days  i   110  15  10 

Ans.  liv.  443     3     5 
9.  What  is  the  interest  of  3255  livres.  for  28  days,  at  l> 
per  cent,  per  month  ? 

^)3255 


16|27   10 
20 

5l50 
12 

16 

6100 
5     6  for  1  month, 

15  daysl 
10    ^^     i 

8 
5 

2     9 
8    '6 

3    "     i 

1 

12     6 

Ans.  liv. 

15 

3     9 

The  present  money  of  account  in  France  is  in  francs  ani 
centimes  or  hundredths. 

in  iNov.  180U,  an  Eni^lish  cruinea  was  worth  25  fr   75  cts, 
A  Spanish  dollar         -  5  do.  65  do* 

P2 


162  EXCHANGE. 

To  change  Francs  to  Livres  Tournois. 
Rule.     Multiply  the  francs  by  81,    and  divide  by    80  fov 
livres. 

EXAMPLE. 

Change  3756  francs  to  livnss. 

3756 

81 

3756 
30048 


850)3U4l>3,6 

38U2  76 
20 


8,0)152,0 

19  Ans.  3802  liv.  19  sols. 

To  change  Livres  Tournois  to  Francs. 
Rule.     Multiply  the  livres  by  80,  and  divide  the  product 
by  81  for  francs. 

example. 
Change  5469  livres  to  francs.  ^ 

5469 
80 


81)4:^7520(5401,48 
405 

325 
324 


120 
81 

390 
324 


660 
648 

12  Ans,  5401  fr.  48  cch» 


EXCHANGE.  163 

To  change  Sols  and  IJeniers  to  Centimes, 

Hvi.K      T:ike  one  half  of   the  ^oh  and  deniers,  as  if  they 
were  iulegei*s ;  this  half  is  the  number  of  centimes  required. 

EXAMPLES. 

sol.  den.     sol.   den.    sol.  den.     sol.    den. 
Chansre  4       6       12       2       6       8       10       6  to  centimes. 


Ans.     23  61  34  83  centmes. 

When  there  i«  a  remainder  in  dividing  the  sols,  it  is  to  he 
carried  to  the  demers,  and  reckoned  10  and  not  12;  add 
this  )()  to  the  deniers,  and  take  one  halt  of  the  sum  for  the 
remaining  centime. 


sol.  den. 
5       8 

EXAMPLES. 

sol.     den. 
15        4 

sol. 
19 

den. 
6    to  centimes. 

•i9 

77 

98  centimes. 

Reduce 

Ans. 

If  thie  number  of  deniers  be  10  or  1 1,  thoy  are  to  be  re* 
jecled,  and  m  place  of  them  you  are  to  add  i  to  the  number 
of  sols  preceding,  and  then  annex  a  cipher  to  it;  oae  half  of 
this  is  the  centimes  required. 


sol.  den. 
Change     1      lu 

EXAAtPLES. 

sol.  den.              sol.  den. 
7     1 1      and     15     1 0  to  centimes. 

2)20 
Ans.        10 

2)80                   2)! 60 
40                       80  centimes. 

Sols  and  deniers  are  reduced  to  centimes  hy  the  preced- 
ing rule  ;  and  though  the  result  is  not  accurate,  yet  from  ite 
simplicity  and  conciseness  it  is  generally  used. 


164 


EXCHANGE. 


TABLES 
For chan^insr  TAvrrs^  Sols  and  Dea'ers  to  Francs  and  Centimes. 
{^N.  B.       The  first  i»   suJBciently  exact  for  business  ;  in  the  seco..d  the 
answer  is  calculated  .o  the  ten-thoudandth  part  of  a  cen!inie.) 


rAbi.K  i 

Tabl 

K   V  i 

10,000th8 

Deniers. 

Fr. 

Cent. 

Fr 

.  Cent, 

.  of  a  I  ent 

1 

- 

0 

0 

'- 

0 

0 

4  5 

2 

- 

0 

1 

0 

0 

8230 

3 

- 

0 

1 

0 

1 

2:.46 

4 

- 

0 

2 

0 

1 

6461 

5 

/ 

0 

2 

0 

2 

0576 

6 

- 

0 

2 

0 

2 

4*;9l 

7 

0 

3 

0 

2 

8807 

8 

0 

3 

0 

3 

2922 

9 

0 

4 

0 

3 

7037 

10 

0 

4 

0 

4 

1:52 

11 

0 

5 

0 

4 

5267 

Sols.  1 

0 

5 

0 

4 

9383 

2 

0 

10 

0 

9 

8765 

3 

0 

15 

0 

14 

8  4S 

4 

0 

20 

0 

19 

7531 

5 

0 

25 

0 

24 

69:4 

6 

0 

30 

0 

29 

6296 

7 

0 

35 

0 

31 

5(>79 

8 

0 

40 

0 

39 

5062 

9 

0 

44 

0 

44 

4444 

10 

0 

49 

0 

49 

3827 

11 

0 

54 

0 

54 

32  0 

12 

0 

59 

0 

69 

2593 

13 

0 

64 

0 

64 

1975 

14 

0 

69 

0 

69 

1358 

15 

0 

74 

0 

74 

0741 

16 

0 

79 

0 

79 

0  23 

17 

0 

84 

0 

83 

9506 

18 

0 

89 

0 

88 

8889 

19 

0 

91 

0 

93 

S272 

Livres.  1 

0 

99 

0 

98 

7654 

2 

1 

98 

1 

97 

5309 

S 

2 

m 

2 

96 

2963 

4 

3 

95 

3 

95 

06  7 

6 

4 

94 

4 

93 

8272 

6 

5 

93 

5 

92 

6926 

7 

6 

91 

6 

91 

3580 

8 

7 

90 

7 

90 

1235 

9 

8 

89 

8 

88 

8889 

10 

9 

88 

9 

87 

6543 

12 

11 

85 

11 

85 

1852 

15 

14 

81 

14 

81 

48 --5 

26 

19 

76 

19 

75 

80S€ 

EXCHANGE. 

^ 

16^ 

10,000th» 

Li^Tci. 

Fr. 

Cent. 

Fr. 

Cert. 

O'   H 

.  eat 

24 

23 

70 

23 

70 

s: 

[)4 

SO 

29 

63 

29 

62 

9(. 

>0 

40 

39 

51 

39 

50 

6 

73 

60 

49 

38 

49 

38 

27 

6 

60 

59 

26 

59 

25 

92 

59 

70 

69 

14 

69 

13 

6803 

72 

71 

11 

71 

11 

11 

11 

SO 

79 

01 

79 

01 

2344 

JO 

88 

89 

88 

,88 

8889 

96 

94 

81 

94    > 

'     81 

48 

5 

100 

98 

77 

''. 

98 

76 

64 

32 

200 

197 

53 

197 

53 

OS 

64 

SCO 

296 

30 

296 

29 

62.97 

400 

395 

06 

395 

06 

1729 

600 

493 

83 

493 

82 

7i 

61 

1000 

987 

65 

987 

65 

4322 

5000 

-     49  3S 

27 

-      4938 

27 

1608 

10000 

.     9S76 

64 

-      9876 

54 

3217 

A    1 

'ABLE 

For  reducing  Francs 

and  Cent 

imes  to  Livres^ 

Sols  and  Dcnkr 

100[hs 

Cent. 

Sol. 

Den. 

of  Uen. 

Francs. 

Liv. 

Sol  Dea 

1       - 

0 

2 

43 

2 

2 

0 

6 

2       . 

0 

4 

S^ 

3 

3 

0 

9 

3 

0 

7 

29 

4 

4 

1 

0 

4       - 

0 

9 

72 

5 

5 

1 

3 

5 

1 

0 

]5 

6 

6 

1 

6 

10      - 

2 

0 

30 

7 

7 

1 

9 

15 

3 

0 

45 

8 

8 

2 

0 

20       - 

4 

0 

60 

9 

9 

2 

3 

25       - 

5 

0 

75 

10 

10 

2 

6 

30 

7 

0 

90 

15 

15 

3 

9 

35       - 

6 

05 

20 

20 

5 

0 

40       - 

8 

20 

30 

80 

7 

6 

45       - 

9 

35 

40 

40 

iO 

0 

SO 

10 

50 

50 

50 

12 

6 

55       - 

U 

65 

60 

60 

15 

0 

60       - 

12 

80 

70 

70 

17 

6 

65       - 

13 

95 

80 

81 

0 

0 

70       - 

14 

2 

10 

90 

91 

2 

6 

75       - 

15 

2 

25 

100 

101 

5 

0 

80       - 

16 

2 

40 

200 

202 

10 

0 

85       . 

17 

2 

55 

300 

303 

15 

0 

90       - 

18 

2 

70 

400 

405 

0 

0 

95       - 

19 

2 

85 

500 
1000 

606 
10  2 

5 

10 

0 
0 

Prunes. 

Liv 

Sol. 

Den. 

5000 

5062 

10 

0 

1 

1 

% 

8 

lOtfOO 

lOil^i 

t 

f 

lU  EXr MANGE 

SPJIJV. 

Spanish  reckonings  are  of  two  sort* : 
Money  of  Plate,  d  siing-nisheti  by  hani  or  >  (are  f\n]hr^^  &C. 
Money  of  Vellon,  d^shng-uished  by  cifrrenf  dollars. 
The  former  is  c>li-j\  por  cent,  above  ttie  letter. 
100  reals  plato  being  equal  to  188y\  reals  vellon. 
100  reals  vellon  -         -  55}  reah  piale. 

17  reals  plate  -         -         32  reals  vellon. 

17  piastres  or  current  dollars     256  reals  vellon. 
4  maravadies         -  make  -  I  quarto. 

8;\  quartos,  or  34  maravadies,        -  1  real. 

The  peso,  piastre,  or  current  dollar  of  8  reals  plate,  pass- 
es at  15  reals  vellon  in  trad«,  but  m  exchange  it  is  estimated 
at  15  reals  vellon  2  maravadies. 

The  ducat  of  exchange  is  375  maravadies. 
The  real  plate  is  estimated  at  10  cents,  and  the  real  vel- 
lon at  5  cents,  in  the  United  States. 
The  Spanish  arobe  is  25  lb. 
100  lb.  of  Spain  is  97  lb.  English. 


To  change  Reals  Vellon  to  Reals  Plate, 

Rule.     Multiply  the  giren  sum  by  17,  and  divide  by  3S 
for  reals  plate. 

EXAMPLE. 

Change  800  reals  vellon  to  reals  plat«. 
800 
17 


32)13f300(425 
128 


80 
64 


160 

160         Ans.  425  reals  plate. 

To  change  Reals  Plafe  to  Reals  Fellon. 

RuLF..     MuH.piy  the  given  sum  by  32,  and  divide  by  l?^ 
for  reals  vellon. 


EXCHANGE.  167 


EXAMPLE. 


f        In  426  reals  plate,  how  many  reals  vellon  ? 

32 

850 
1275 


17)13600(800 
136 


00  Ans.    800  reals  vellon. 

To  change  Reals  Plate  and  Reals  Vellon  to  Federal  Money. 

JRuLE.     Multiply  the  reals  plate  by  10,  and  the  reals  vel- 
lon by  5,  for  the  cents  in  the  given  sum. 

EXAMPLES. 

1.  Change  14938  reals  plate  to  Feileral  money. 
14958 
10 


1495,80     Ans.   1 495  dolls.  80  cts. 
2.  Change  17593  reals  vellon  to  Federal  money. 
J  7593 
5 


879,65         Ans.  879  dolls.  65  cts. 


CADIZ. 

Accounts  are  kept  by  some  in  hard  or  plate  dollars^  reals  vellon^ 
and  quartos. 

8^  quartos         -         make         -  1   real  vfllon. 

2U     reals  vellon         -         -  -  1  dollar  of  plate. 

Others  keep  their  accounts  in  reals  plate  and  maravadieS| 
reckoning  34  maravadies  to  1  real  plate. 

To  bring  Reals  Plate  to  Dollars, 

Rule.     Multiply  the  given  sum  by  32,  and  divide  by  17, 
for  reals  vellon,  and  divide  the  reals  vellon  by  20  for  dollars. 


168  EXCIIVNGE. 

EXAMFLK. 

In  320  reals  plate,  howmau^  hard  dollars? 
32 


640 

960 


17)10240(602  reals  velloi>. 
102 


40 
34 


8|-  2;0)60|2  reals  vellon. 

17)51(3  quartos.         dolls.  30  2  3 
15 

Ans.  30  dolls.  2  r.  v.  3  q. 

To  change  hard  Dollars  to  Reals  Plate. 

"Rule.  Multiply  the  dollars  by  20  for  reals  vellon,  and  the 
reals  vellon  bf  ni^  mnitipl;ed  by  17  and  divided  by  32  ^^e 
the  reals  plate  required. — Or,  multiply  the  dollars  by  iOf 
for  rtals  piate. 

''example. 

In  16  hard  dollars  how  uiany  reals  plate  ? 

16  Or  thus,     16 

20  lOf  16 

3:,^^  160  — 

17  10  8)80 

2210  17U -R.  P.  10 

320 


J2)5440(170 
32 

S:21 

224  Ans.  no  reals  plate. 


EXCHANGE.  160 

PRACTICAL  qUESTIOA'S. 

The'answers  io  xMch  are  in  Dollars^  Reals  Fellon  and  Quartos. 
1.  Whnt  will  45940  pipe  staves  come  to  at  8    piastres  or 
current  dollars  per  M.  or  UOO? 
45940 
80 


12|00)36752tOO 


3062|    current  dollars, 
8      reuls. 


24501 1    reals  plate, 

3S 


49002 
73503 
lOf 


17)78404^1(46130 
68 

104 

lOi 


17  8,0)46  It^O 

u         Mih  nm  0  1 

34 

ii 

n)§^l(i 
\i 

5|       Am.  9306  Ufi  M\9.  0  r..  1  q. 

jpml,  ^.    r,    Q- 

%^  81800  ha?fel  atw^l  at  30J  p^p  IgOO         411     3    7 

a,  1200  hh'i        do,         40        c|q,  so     2    3 

4t  I  ^si^s  §h§?ry  wir\§     30    pev  e'^^k  45    3    4 

H 


170  EXCHANGE. 

The  result  of  the  following  is  in  Reals  Plate^  and  Moravadies. 

5.  In  610  hard  dollars,  how  many  reals  plate  ? 
010 
20  reals  vellon=:l  hard  dollar. 

12200 

85400 
12200 


32)207400(6481 
192 


154 

128 

260 
256 

40 

32 

8  Ans.  6481  reals  plate  8  mar. 

6.  What  will  2632  barrels  of  flour  come  to  at  1 1  current 
dollars  per  barrel  ? 
2632 
11 


28952  piastres  or  current  dollars. 

8  reals  plate=l  piastre  or  current  dollar. 


Ans.  231616  reals  plate. 
7.  88  lasts  of  white  dry  salt,  at  6  piastres  per  last? 
88  , 
6 


528 
8 


4  2'M  Ans.  4224  reals  plate 


EXCHANGE.  171 

8.  Change  £600  sterling  to  reals  plate,  exchange  at  36i(i. 
sterling  per  piastre. 


600 
20 

12000 
12 


561      144000 
4  4 


146  )  576000  (  3972  current  dollars. 
435  8 


1410        31776 
1305  3   10 


1050        31779   10 
1015 


350 
290 

60 
8 


145)480(3  reals. 
435 

45 

34 

180 
135 

145)1530(10  maravadies. 
145 

80  Ans.  31779  reals  plate,  10  mar. 

9.  In  £3200  sterling  how  many  reals  plate,  exchange  ai 
36ic/.  sterling  per  piastre  ?  Ans.   169489  r.  p.  22  mar. 

'  N.  B.     In  St-  Lucar,   accounts  are  kept  in  reals  plate  and  quartq^ 
16  quartos  to  i  real  plate. 


172  EXCHANGE. 

BILBOS. 

Accounts  are  kept  in  Reals  Vellon  and  Maravadies^  34  mar«- 
vadies  making  1  real. 

The  pound  in  Bilboa  consists  of  17  oz.  except  in  iron, 
which  is  but  16  oz. 

32  veltB  are  equal  to     66  gallons  in  the  U.  States. 
100  fanagues         -         152  bushels  do. 

100  varas  -         lOB  yards  do. 

To  change  Piastres  or  Current  Dollars  to  Reals  Plate, 
Rule.     As  1  current  dollar  is  to  15  reals  2  maravadies,  so 
is  the  given  sum  to  the  reals  required :  or  multiply  the  sum 
by  15  reals  2  maravadies,  for  reals. 

EXAMPLE. 

In  6000  current  dollars,  how  many  reals  vellon? 
2=r  J^)5000  Or  tlius,.        5600 

15  2=1  curr.  doll.  2 


25000  34)10000 

5000  

294     4  294     4 


75294  4  Ans.  75294  reals  vel.  4  mar. 

To  change  Current  Dollars  to  Sterling, 
Rule.     As  1  dollar  is  to  the  rate  of  exchange,  so  is  the 
l^lven  sum  to  the  sterling  required. 
example. 
In  5000  piastres  or  current  dollars,  how  many  pounds  ster- 
ling, exchange  at  36f  per  dollar  ? 
p,  d.  p. 

Aa  1     :     36J     ::     5000 
36f 


180000  5000 

1875  ^  3 


12)181875  8)15000 

210)1 5 1 5|6  3  1876 

Ans.  £.757  16  3 


EXCHANGE. 


178 


To  chancre  Sterling  to  Current  Dollars, 

!RtTLE.     As  the  rate  of  exchange  is  to  1  dollar,  so  is  the  given  suim 
to  the  dollars  required. 

EXAMPLE. 

In    £757  165.  Sd,  sterling,    liow  ma»y  current  dollars,    exchange  at 
S6jd.  sterling  per  dollar  I 

d.  doll.  £      s     d. 

As   361       :     1      :  ;    757     16  3        Ans  5000  cur.  dolls,  or  piastres. 

To  change  Sterling  to  Reals  Ft  lion. 
Rule.     As   the  rate  of  exchange  is  to  15  reals  2  maravadies,    so  is 
the  given  sum  to  the  reals  required. 

example. 
In  £436    10s.  sterling,  how  many  reals  vellon,,  exchange  at  B6ld: 
sterling  per  current  dollar  1 


d.             r.  m.             £     s. 
As     363      :     15  2     :  :     436  10 

8                                   20 

291                               873« 
12 

104760 

8 

2  mar.=  1       838080 

'^            152. 

Or,     83808a 
2 

4190400 
8380S0 
49298 

34)1676160  mai%. 
49298  reals' 

291)12620498(43360 
1164 

980 
873 

1074 

873 

2019 
1746 

2- 38 
20*9 

119 
34  mar.=l  reil. 

291)4046(13                   Ans 

.  48369  reals  13  ai^ 

Q2 


174  EXCHANGE. 

PRACTICAL  qUESTIOJVS. 

1.  What  will  122  quintals  offish  come  to  at  136  reals  per 
quintal  ? 

136 

732 
366 
122 


An?.   16592  reals. 
S.  What  is  the  cranage  of  1 137  quintals  offish  at  10  ma- 
ravadies  per  quintal  ?  Ans.  334  reals  14  mar. 


BARCELO.N-A. 

The  moneys  of  account  in  Barcelona   and  throughout  the  pro- 
vince of  Catalonia  are  Livres^  Sols  and  Deniers, 

12  deniers         -         make         -         1   sol. 
20  sols  -         -         -       -         -     1    hvre. 

37 1  sols,  or  IJ  lirre  •         -         1   hard  dollar. 

28  sols      -         .       1  curr.  doll,  the  piast.  of  exchange. 
To  change  Ldvres  to  hard  Dollars, 
Rule.    Divide  the  livres  by  3  and  then  by  5,  and  add  the- 
two  quotients  together,  for  hard  dollars. 

EXAMPLES. 

1.  How  many  hard  dollars  in  360  livres  ? 
3     360 

120 

72 

192  An».  102  hard  dollarn, 

2.  How  many  bard  dollars  mtist  be  paid  for  an  invoice  o/ 
foods amoootin^  to  7134  livres? 

3     7134 


Am^  3S04  b,  do]l«,  30  «ofc 


EXCHANGE.  17i 

To  change  Hard  Dollars  to  Livres, 
Rule.    Add  to  the  given  siim  the  half,  quarter  and  eighth 
of  it,  and  the  sum  will  be  the  livres  required. 

EXAMPLKS. 

1.  In  192  hard  dollai-s,  how  mmy  livres 

192 

48  I 


24 


360  Ans.  360  livres, 

2.  How  many  livres  in  3804|  hard  dollars  ? 
3801,3 
1 902,4 

9j1,2 

475,6 


7134,0         Ans.  7134  livre». 

To  change  Livres  to  Current  Dollars. 

Rule.     Multiply  the  livres  by  5,  and  divide  that  product 
by  7,  for  current  dollars. 

EXAMPLE. 

Change  2716  livres  to  current  dollars, 
2716 
5 

7) 1358a 

1940  Ans,  194a  cur.  dolls-. 

To  change  Current  Dollars  to  Livres. 
HtJLE.     Multiply  the  current  dollars  by  7,  and  divide  the 
product  by  &,  for  iivres. 

EXAMPtK. 

Change  1040  current  dollars  to  Uvref. 
Ji)40 
T 


6)U5f>cja 


27ia 


An?.  §716  ;iTr«^». 


17S  EXCHANGE. 

P0RTUG./1L, 

Accounts  ore  kept  in  Alilbeos  i\n  (  Hcus^  reckoning  1000  reas  to  1 
Tuiltrea  ofbs.  7-^i/.  strrling^  or  I  Joll.  25  cts.  in  the  U.  States. 
A  vinten  is  20  rt;as,  and  5  vintens  is  a  festoon  of  100  reas. 

FXAMI'I.KS. 

1.  Changfe  579  millreas  740  reas  to  Federal,  at  1  doll.  26 
Cts.  per  mxilrea.  m.    r. 

579,7  10  Or  thus,  579,740 

1,25  i  added  144,935 

2898,700  dolls.  724,675 

69568,80 


cents  7i>'167,5  0  Ans.  724  dolls.  674  cents. 

2.  Change  7:24  dolls.  67i  cts.  to  millreas,  at  1  doll.  25  cts. 
per  millrea. 

1,25)724,675(579  mill.  740  reas. 
Or  dedurtinjg^  i  from  the  sum  in  Federal  money  gives  the 
millreas,  4«c. 

EXAMPLE. 

i)724,675 
144,9.35 

579,740  as  before. 

3.  Change  579  millreas  750  reas  to  sterling,  at  5^.  7J<I^ 
par  millrea. 

579,760 
67J 

4058,250 
31785,00 
289,875 

12)39153,125 

2|0)320ll      I 

Ans.  £163   I      1} 

4.  In  £163  1    1|  sterling  how  many  millreas,  at  bs,  7Jci. 


per  millrea^ 


s.     d.  reas.  £       s.     d. 

%     7i     :     lUOO     ::      K33     1      1^- 

Ans.  579  millreas  750  rea». 


EXCHANGE.  177 

5.  What  is  the  commission  on  6245  mill.  46  reas,  at  2^ 
per  cent? 

6245,046 

21  per  1,00 


12490092 
3122523 


156,12615  Ans.  156  mill.  126  reas. 

6.  Suppose  a  cargo  is  soW  for  6245  millreas,  at  2  months 
credit,  for  prompt  payment  of  which  ^  per  cent,  per  month 
is  allowed  ;  how  much  is  the  discount  ? 
i)6245  Or  thus, 

^  per  cent,  far  2  months=l  per  cent. 

31,225  for  1  month,  6245 

2  1 


Ans.  62,450  for  2  months.  62,45 

7.  Suppose  you  import  59G0  hhd.  staves  and  5060  barrel 
staves,  on  which  there  is  a  duty  of  23  per  cent,  which  is  ta- 
ken in  kind,  how  many  of  each  remain  for  sale  ? 

Ans.  4590  hhd.  and  3897  bbl. 


m.    r. 

m.      r. 

8. 

702  barrels  of  flour  at     8  600  per  bbl. 

6037, xH)0 

9. 

4590  hhd.  staves         -            030  per  stave 

137,700 

10. 

3897  barrel  do.            -            020  per  do. 

77,940 

11. 

71  alquiers  of  beans           480  per  alquier 

34,080 

MEASURES    OF    POR'I'UGAI** 

Cloth  Measure, 

A  vara  is  43|  inches  English. 
A  covedo  is  26^  do. 

Wine  Measxtre, 

1  almude  is  12  canadoes. 

1   canado  is  4  quarteels. 

An  almude  is  4^  gallons  English  wine  measure. 

A  canado  is  d  pints  English. 


178  EXCHANGE. 

Corn  Measure. 

1  moy  is  16  fangas. 

rfanga  is  4  alquiers. 

1  moj  of  60  alquiers  is  3  English  quarters,  or  24  bushels 
Winchester  measure. 

1  quarter  is  20  alquiers. 

1  English  bushel  is  2|  alquiers  in  Lisbon,  2  alquiers  in 
Oporto,  and  2|  alquiers  in  Figuiras. 

A  ino}'  of  salt  is  the  same  measure  as  corn. 

A  pipe  of  coals  is  16  fangas. 

1  fanga  is  8  alquiers. 

A  pipe  of  coals  is  \  28  alquiers,  which,  at  2^  alquiers  per 
bushel,  is  51^  bushels  English. 

Weights  of  Portugal. 

1  quintal  is  4  arobes. 

1  arobe  is  32  pounds,  so  that  a  quintal  is  128  lb.  Portugal 
wt.  which  is  equal  to  about  132  lb.  English,  avoirdupois  wt. 
A  pound  is  about  16i  ounces  English. 

Loss  by  exchanging  English  money  in  Portugal. 

An  English  guinea  passes  at  Lisbon  for  3  m.  600  r.  which 
is  134  reas,  or  9  pence  less  than  the  value. 

An  English  crown  passes  for  800  reas,  which  is  89  reas, 
or  6  pence,  less  than  the  value. 

An  English  shilling  passes  for  160  reas,  which  is  18  reas 
or  about  1^  penny  less  than  the  value. 


LEGHORJY. 

Accounts  are  kepi  in  Piastres^  Soldi  and  Denari^  reckoning  1 1 
deniers  to  1  soldi^  and  20  Soldi  to  1  piastre  or  dollar  of  4^d. 
sterling  at  par. 

1|  paul,  or  2  sols,  are  equal  to  1  livre. 

6    livres         -         -         .        .  i  piastre  or  dollar. 

5J  livres  (effective  money)     -  1     do. 

1  ducat  .         -        ^         .  1 1    do* 


EXCHANGE.  179 

Weights. — A  pound  is  only  12  oi!ncei=,  in  all  commodities. 

145  lb.  In  said  t(>  be  eqnal  to  the  English  quintal  of  112  lb. 
but  tish  geno.rally  renders  about  Ii»6  (o  138  lb.  per  quintal. 

145  lb.  m  Leghorn  makes  112  lb,  in  the  United  States. 

4  brasses         -         -         -         -  i  cane. 

^  ^   100  brasses     -         -         -         -         64  yardii  U.  States. 

1  palm  -         -  -         ^5  incbes  do. 

4  sacks  are  2  per  cent,  less  than  an  English  quarter,  of  8 
bushels. 

EXAMPI.KS. 

1.  Hovf  much  will  5630  lb.  of  ginger  come  to  at  9  pias- 
tres per  100? 

5f530 
9 

50ii|7O 
20 


14100  Ans.  596  piast.  14  sol. 

2.  What  will  9764  lb,  of  pepper  come  to  at  27]    ducats 
per  100? 

9750 

271 


G8320 
19520 
2440 

^)265960 
4432GI 


piast.  3102|86| 
.    20 

soldi  171^31 
12 

den.  4|00 

Ans.  3102  piast.  17  sol.  4  den. 


100  EXCHANGE. 

3.  What  will  143700  lb.  of  pitch  come  to  at  26  pauls  per 
100? 
Note.     One  paul  is  equal  to  |.  of  a  livrc. 
143700 
26 


862206 
287400 


37o62,00  pauls. 
2 


3)74724 

6)24908  livres.. 

4151  6  8 

Ans.  41 5J  pinst.  6  sol.  3  den. 

4.  TTnvv   m^irb   will  4200  saclis  of  wheat  come  to   at  26 
Uvres,  tiliccuvM  mgnt  y,  pt  r  Rnck  ? 
42n0 


gfj^OO 
8400 


liv,      piff^t, 


5 3     J     I       \  \        lOB^OO  livros. 

*  Ang,  10U9)  plnst.  0  sol  \  de«, 

5.  too  barre^l^  pork  16  pinstrfs  per  barrel  )BUQ 

6.  lOUO     c]o/     flour  10|     do,  do,        lU^OO 

7.  !^tim»  lb,  coifee  ^tr  do.  per  100  691  12  0 
0.  6570  lb.  pimonte  18  dt..  do  1184  0  0 
9.  0370  lb,  rice  24  liv,  eur  mf>n  pr.ieo  374  10  0 

JO  dl'Uli)  lb,  loj^wood  U  pJH^tres  per  lOOO     1^50  0  4 

JU  4170  Uk  Rua.  wan  3q  ducats  p^r  100        11^9  15  6 

n\  104060  lb.  mgnr  tiO  pjpgfreg  per  151  lbjMG74  3  6 

1:3.  33biMb  lo»f*oprgO      de,     p^r  lOO       1005  0  0 

IJ,  lOOOeHsUstur  4i     do.      per  cnek      4500  0  0 

15.  lOOOUO  lituves  t)'     uo.       per  100       4000  0  0 


EXCHANGE.  181 

JVJPLES. 

Accounts  are  kept  in  Ducats  and  Grains^  reckoning  100  grains 
to  1  ducat. 

The  current  coins  are  grains,  carlins,  ducats,  dollars,  and 
ounces. 

10  grains  make  I  carlin ;  10  carlins  1  ducat;  3  ducats  1 
ounce. 

The  Naples  dollar  passes  for  120  grains,  and  the  Spanish 
dollar  for  126  grains. 

100  lbs.  Naples  weight  are  equal  to  64f  lb.  English. 

Brandy  is  sold  per  cask  of  12  barrels,  or  132  gallons:  60 
karafts  make  a  barrel. 

Sewing  Silks  are  sold  per  lb.  of  12  ounces. 

Lustrings  are  sold  per  cane  of  84  inches. 

Sugar,  coffee,  fish  and  tobacco  are  sold  per  cantar  of  196 
lb.  in  the  United  States. 

The  cantar  is  subdivided  into  100  rotolas  of  33  ounces  each. 


EXAMPLES. 

1.  What  is  the  amount  of  10  casks  6  barrels  29  karafts  of 
brandy,  at  92  ducats  per  cask  ? 
92 
10 

6bbl. 
20  kar. 
5  do. 
4  do. 

920 
i     46 
T^a        2  55 
1            64  nearest. 
i            51 

909  70        Ans.  969  ducats  70  grains. 
2.  What  is  the  amount  of  2  casks  of  clayed  sugar,  weigh- 
ing neat  10  cantars  51  rotolas,  at  65  dollars  per  cantar? 
rot.         dolls.  rot. 

100     :     65     ::     1051  Or  thus,         65 

65  10 


5255 
6  506 


650 

50  rot. 

i  32 

50 

1  do. 

I 

57 

65 

due.  683  15 
Ans.  683  ducats,  15  grains. 


1£ 


EXCHANGE. 


3.  How  much  is  the  amount  of  1  box  of  scented  soap, 
containing  100  parcels  of  16  ounces  each,  at  22  grains  per 
rotola? 

100 
16 

oz.  gr.  

33    :      22     :  :  1600  oz.        Ans.   10  ducats,  66  grains. 

4.  What  is  the  commissson  on  996  ducats,  at  2  per  cent.  ? 

Ans.   19  ducats,  92  grains. 


ducats. 

73     per  cantar 


can.  rot. 

5.  3  73  of  coffee     - 

6.  16    19|     soap         -         -  21 

7.  1  59  do.  -  -  21  "  " 
0.  7  97f  do.  -  -  21  "  " 
9.              67L  scented  do.          -  30  ''       '^ 

10.  52     white     do.          -  17  "       '' 

11.  7  64  raisins         -          -  12  "       " 

12.  2  casks  1 1  bbls.  4  kar.  brandy  102  per  cask 

13.  10  do.  43   do.  do.  92  "  " 

14.  9  do.       12  do.  do.  92  ''  " 


15.  355  canes  of  silk 


2  50  per  cane 


due.  gr. 
272  29 
340  14 

33  39 
167  52 

20  25 

8  84 

.  91  68 

298  06 

82  16 

70  53 
887  50 


TRIESTE. 

Accounts  are  kept  in  Florins  and  Kreutzers — 60  kreutzers  make 
1  Jlorin. 

The  exchange  on  London  (8th  July,  1803)  was  12  florins 
for  the  pound  sterling. 

The  other  kinds  of  money  are  Soldi  and  Livres. 


make 


1 


1 


livre. 
florin. 


20  soldi 
o\  livres  - 
100  lb.  Vienna  weight=123  lb.  Avoirdupois. 
A  brace  is  27  inches,  or  J  of  a  yard  English. 
A  barrel  of  wine  is  18  gallons. 

A  staro  of  wheat  is  2|  bushels  nearly — 3^  staros  is  equal 
to  an  English  qtiarter  of  8  bushels. 

Sales  and  purchases  are  usually  made  in  bills  on  Vienna 
at  3  months  date. 


EXCHANGE.  183 

EXAMPLES. 

1.  What  is  the  amount  of  263  lb.  Vienna  weight,  of  soap, 
at  22  kreutzers  per  lb.  ? 

263 

22 

526 
526^ 

6|0)578|G 

96  26         Ans.  96  flor.  26  kreutzers. 

2.  758  gallons  wine,  at  21  florins  30  kreutzers  per  barrel? 

758 
21 


758 
1516 


30  kr.  i        379 


18)16297(905 
162 


97 
90 

7 
60 

18)420(23 
36 

60 
54 

6  Ans.  905  flor.  23^  kp. 

Ji,  kr.  Ji.    kr, 

3.  120  stares  of  wheat  at  4  20  per  staro  Ans.  520  00 

4.  715  braces  of  silk         3    50  per  brace  2740  50 

5.  1730  lb.  coffee                   58  per  lb.  1672  20 


184  EXCHANGE. 

GENOA. 

Accounts  are  kept  in  Denarii^  Soldi  and  Fezzos^  or  Lires. 

12  denarii         -         -         make  1    soldi. 

20  soldi  -         -        -        -         1   pezzo  or  lire. 

1  pezzo  of  exchange       ^         -         53  lires. 
The  course  of  exchange    is  various — from  41d.  to  bSd. 
sterling  per  pezzo  or  lire. 

In  Milan,  1  crown  =    60  soldi  of  Genoa. 

Naples,         1  ducat  =    86  do. 

Leghorn,      1  piastre=    20  do. 

Sicily,  1  crown  =  127|        do. 

To  reduce  Exchange  Money  to  Lire  Money. 
Rule.  Multiply  the  exchange  money  by  5J  for  lire  money. 

EXAMPLE. 

fn  384  pezzos  of  exchange,  how  many  lires? 
384 


1920 

192 

96 


2208  Ans.  2208  lires. 

To  reduce  Lire  Money  to  Exchange. 
Rule.     Multiply  the  lire  money  by  4,  and  divide  the  pj^o- 
duct  by  23,  for  exchange. 

EXAMPLE. 

In  2203  lires,  how  many  pezzos  of  exchange  ? 
2208 
4 


23)8832(384 
69 


193 
184 


92 
92 
—    Ans.  384  pezzos  of  exchange. 


EXCHANGE.  18& 

To  reduce  hires  to  Sterling. 
Rule.     As  1   lire  is  to   the  rate  of  exchange,  so  are  the 
lires  to  the  sterling  required 

EXAMPLE. 

In  360  lires  how  much  sterling,  exchange  at  54d.  sterling 
per  lire  ? 

1      :     64     ::     360 
54 


1440 
1800 


12)19440 


2|0)I62|0 

81        Ans.  £81   0  0  sterlings. 

VEMCE. 

Venice  has  three  kinds  of  money,  viz.  Banco  money,  Ban- 
co current  money,  and  Picoli  money.  Banco  money  is  20 
per  cent,  better  than  banco  current,  and  banco  current  20 
per  cent,  better  than  picoli. 

The  different  denominations  of  money  are  Denarii,  Soldi, 
Grosi,  and  Ducats. 

12  denarii,  or  deniers  d'or,  make  1  soldi,  or  sol  d'or. 
5J-  soldi     ►         -         -         -  1  gros,  or  grosi. 

24  gros,  or  grosi     -         -         -      1  ducat. 
100  ducats  banco  of  V^enice,  in  Leghorn  =  93  pezzos. 
do.  Rome       =  68^  crowns, 

do.  Lucca       =  77       do. 

do.  Frankfort  =  139}  florins. 

The  par  of  exchange  in  1798  was  54|c/.  sterling  per  ducat 
banco. 


R2 


186  EXCHANGE. 


How  much  sterling  is  equal  to  2712  ducats  banco,  ex- 
change at  bO^d,  sterling  per  ducat  banco  ? 
due.         d.  due, 

1     :     501      ::     2712 
4  201 


201  2712 

54240 


4)545112  farth. 
2|0)1135|6  6  shillings. 
Ans.  £567  16  6  sterling. 


SMYRJVA. 

Accounts  are  kept  in  Piastres  and  hundredths^  except  the  English 
accounts.^  which  from  ancient  custom  are  kept  in  piastres  and 
eightieths  or  half  paras. 

The  fractional  parts  are  sometimes  called  aspers,  100  as^ 
pers  to  1  piastre. 

The  following  calculations  are  made  in  piastres  and  hun- 
dredths. 

A  piastre  is  equal  to  40  paras,  and  a  Spanish  dollar  to  136 
paras. 

340  piastres  are  equal  to  100  Spanish  dollars. 
The  exchange  on  London    was  13  piastres  for    1  pound 
sterling,  May  1 4th,  1800. 

Their  weights  are  the  Rotola,  Oke,  Checque  and  Tiffee. 
A  rotola         -         -     marked  Ro.  is  IbQ  drams. 
An  oke     -         -         -         ^y^  400  do. 

A  cheque  of  opium         -  -  250  do. 

do.       of  goats  wool       -         -      800  do.  or  2  okes. 
Atiffeeofsilk       -         -         -  610  do. 

100  rotolas,  or  11500  drams,  or  45  okes,  are  a  quintal  of. 
this  country. 

112  lb.  English  should  render  here  40|  oke?r,  or  90f  roto- 
las.    45  okes  of  this  country  render  123f  lb.  English. 
A  pike  is  27  inches  nearly. 


EXCHANGE.  187 

To  change  Piastres  to  Dollars. 
Rule.     Multiply  the  piastres  by  5,  aad  divide  the  product 


f  17,  for 

cents. 

EXAMPLE,^ 

Change 

1277/^, 

] 

;  piastres  to  dollars. 
1277,55 
5 

17)6387,75(375,75 
51 

12S 

119 

97 

85 

127 
119 


85 

85         Ans.  375  dolls.  76  ct^ 
To  change  Dollars  to  Piastres. 
Rule.     Multiply  the  dollars  by  3|  for  piastres. 

EXAMPLE. 

Change  375  dollars  75  cents  to  piastree, 
375,75 
31 


1127,25 


75,15  >    r    • 
76,16;    ^"^f 

Ans.    1277,55  piastres. 

PRACTICAL  qUESTIOJSrS. 

I.  How  much  will  lOserons  of  cochineal  come  to,  weigh- 
ij3g  neat  1^1  okes  73  rotolas,  at  80  piastres  per  oke  ? 
724,73 
80 


Ans.  57978,40  piastres^. 


188  EXCHANGE. 

2.  299,  bags  of  sugar,  weighing  506  quintals    96  rotolas, 
tare  J  4  rotolas  per  bag,  at  1 10  piastres  per  quintal  ? 
gross     50G     96  299 

tare         41     86  14 


neat      465     10  1196 

110  299 


Ans.     51161     00  piast.  100)4186 

41   86 
3.  4  cases  of  opium,  weighing  gross  1026  rotolas,  tare  84 
okes  75  rotolas,  at  10|  piastres  per  cheque. 

Note.     1  rotola  is  equal  to  /^  of  an  oke,  and  I  oke  to  1| 
cheque. 

rot.     1026 
9 


gross  okes 
tare 

20)9234  rot. 

461   70 
84  75 

neat  okes 

37t3  95 
If 

C76  95 
3 

376  95 
226    17 

5)1130  85 

c)9R    17 

cheques     G03   12 
lOf 

6031  20 

5lii    o6 
150  78 

Ans.  piast.  6483  54  # 

4.  893  pieces  of  copper,  neat  okes  19743,85,  at  J|  op  ,76; 
paras  per  oke  ?  o.       r. 

19743,85 

70      ' 


4|0)l382O695l0 
piast,  34^51,73 


EXCHANGE.  189 

5.  What  is  the  custom-house  duty  on  19740  okes  of  cop- 
per at  21,  agio  at  2^  per  cent.  ? 

To 

Note.     The  charges  are  all  established  by  a  tariff  of  the 
Levant  Company. 

19740 
2^ 


39480 
9870 

4|0)4935|0 

agio  2i=jV)l  233,75  amount  of  duty  at  2^  par<v5* 
30,84  agio  at  21  per  cent. 

Ans.  piast.  1264,59 

0.  English  consulage  on  430  quintals,  at  5^  piast.  agio  7 
per  cent. 

430 
5i 


2150 
216 

2365 

7 


Ans.  piast.   165,55 

7.  Custom-house  duties  on  88  quintals  90  rotoias,  at  ^y^* 
agio  21  per  cent. 

88,90 
20 


11|0)17780|0 

24=yV)16,16 
,40 

Ai>s.  piast.  16,56 


190  EXCHANGE. 

8.  What  will  the  following  charges  amount  to,  viz.  porter- 
age /^jy,  house  porters  5*^,  weighing  /„ ,  chan  duty  Z^,  visit- 
ing and  marketing  ^'^  per  quintal  on  438  quintals .? 


porterage 
house  porters 

8 
4 

438 
17 

weighing 
ehan  duty 
visiting 

2 
2 
1 

4J0)744|6 

— 

Ans. 

piast.  186,15 

17 


PALERMO  LY  SICILY. 

Accounts  are  kept  i?i  Onges^  Tarins  and  Grains. 

20  Grains         -         make         -         1  Tarin. 
30  Tarins        .         -         -       -         1  Onge  or  Once. 
Feb.  6,  1 803,  the  value  of  the  money  of  Palermo  in  U.  S. 
currency  was  as  follows  : 

equal  to       -       -         4  Mills. 
-     -       =       -       -         8  Cents. 
1     Sc.  doll.    ==     -       96     do. 
21  do.  =  1  Onge  =  240     do. 
The  Spanish  dollar  is  current  at  252  grains.     The  value 
of  the  onge,  at  par,  is  II5.  3d.  sterling.     The  exchange  on 
London,  Feb.  3,  1 803,  was  56  tarins  for  the    jt  sterling,  or 
lOs.  S^d.  sterling  per  onge. 

The  Cantar  of  Sicily     =     176     lb.  Avoirdupois. 
The  Hottoii  -         =  If  lb.  do. 

100  Rotloii  make  a  Cantar. 
A  Cantar  of  oil  is  25  gallons  English  measure.     The  Sief- 
lian  barrel  contains  9  gallons. 

Mahogany  is  sold  by  weight ;  one  foot  board  measure  will 
weigh  about  2  rottoli. 

The  measure  called  Caffis  is  3^  gallons. 
The  lb.  in  Sicily  is  J  2  oz.  Avoirdupois. 
The  Salm  is  485  lb.  Avoirdupois. 


1 

Grain 

20 

do.  =     1    Tarin 

240 

do.  =  12     do.  = 

600 

do.  =  30     do.  = 

EXCHANGE.  191 


EXAMPLES. 


1.  What   cost  264  cantars   25  rottoli  of  mahogany,   at  8 
onges  15  tarins  per  cantar? 


264 
8 


2112 

15  tar. 

^ 

= 

132 

25  rot. 

i 

= 

2 

3 

15 

2246  3   15 

Ans.  2246  ong.  3  tar.  15  gr. 

2.  A  cargo,  consisting  of  3564  quintals  offish,  invoiced  at 
5  dolls.  50  cts.  per  quintal,  is  sold  in  Palermo  at  75  per 
cent,  advance  :  what  sum  must  be  received  for  it  at  252 
strains  per  dollar  ? 

3564 
5 


17820 
50  cts.  1  =  1782 


19602 
50  per  ct.  -J  =  9801 
25     -     -    i,  =  4900  50 


dolls.  34303  50 
252 


68606 
171515 
68606 
50  cts.  i  =         126 


210)864448|2  grains. 

3|0)43222|4  2 

14407   14  2 

Ans.  14407  ong.  14  tar.  2gr. 


192  EXCHANGE. 

3.  What  is  the  brokerage  on  13131  ong.  12  tar.  at  1|  per 
cent.  ? 

13131    12 
1 


13131    12 
1641    12  16 

147172  24   16 
30 

21|84 
20 

16|95 

Ans.  147  oTig.  21  tar.  16  gr. 


ENGLISH  WEST-INDIES. 

Accounts  are  kept  in  Pounds^  Shillings  and  Pence. 

JAMAICA  AND  BERMUDAS, 

The  Spanish  dollar  passes  at  6s,  Sd. ;  3  dollars  are  equal 
to  20  shillings,  or  1  pound,  Jamaica  currency. 

To  change  Jamaica  Currency  to  Federal. 

Rule.  Multiply  the  pounds  by  3  for  dollars.  If  there  be 
shillings,  &,c.  increase  the  pence  in  the  given  sum  by  ^  for 
cents. 

EXAMPLES. 

1.  When  lumber  is  sold  in  Jamaica  at  £16  per  M,  how 
much  is  it  in  Federal  money  ? 

15 
3 

Ans.  45  dollars. 


EXCHANGE.  193 

^.  Change  £54  I'l".  1 1./.  Jam.iica  currency  to  Federal. 
b\     12     11 
20 


1092 
12 


1)13115 

3..:  18  J 


1»^3,933  Ans.   1^3  flollg.  9P.?  cents. 

3.  What  will  102,8  '6  feet  of  boards  come  to  at  £l5perM? 
102,896 
15 


514480 
102H96 

£1543,140 
20 


«.8,8v)0 
12 

I  rf.9,G00  Ans.  £1543  8  9 

r  4.  Whnt  will  5  Uh4s.  of  sno^ar  come  to,  weighing  ^519  lb. 

neat,  at  70  shillings  per  llH)  ib.  ? 
8519 
70 


2|0)59G|3,30 


Ans.  £298  3  3 
5,  How  much  will   5  hhdg.    of  su§far  come  to,   weighing 
9103  lb.  neat,  at  75  shillings  per  100  lb.? 

9103 
75 


45515 
C3721 


2!0)6ft2|7,25 
Ans.  £341^7  3 


S 


194  EXCHANGE. 

BARBADOES. 
The  Spanish  dollar  is  (^s.  Sd.  Barbadoes  cnrrftncy. 

To  change  Barh&does  Currency  to  Federal. 
Rule.  Increase  the  pence  in  the  given  sum  hy  ^  for  cents. 

EXAMPLE. 

(Ihan,^e  £\9     lis.     \0d.  Barbadoes  money  to  Federal. 
£19     11      10  Proof    1)151^691  cents. 

20  39G7i 


991  12)1191)2  pence. 

12  

2lO)99|l      10 


011902 


39671  £49      11      10 


1bb.)iS9^  Ans.  158  dolk.  09 J-  cents. 

Other  calculations  as  in  Jamaica. 


MARTLYICO^  TOBAGO  A^''D  ST.  CHPISTOPHEE'S. 

These  islands  being  inhabited  hy  French  and  English^  the  /(.rrner 
keep  their  accounts  'in  Livre'^y  Svls  arid  DtJiitrs,  and  the  latter 
in  Fou7ids,  Shillings  atid  Pence. 

I\  curieHf.  dollar  is  Bs.   3d. 

A  rounrf  dollar  pn««es  for  Or. 
When  payment  of  freight  or  goods  is  r};eniioi  ed  in  Ppr^rish  dollars, 
disagreement  reij]»eerir.g  /}  eir  value  has  frequeiitlv  i^r'iyer  :  :  i  v  o  }>,t^  fnt 
it  some  persons  disiin^-ui-h  tj  em  hy  round  and  cwninl  CoWcn  ;  o.l  ers 
mention  the  hits  to  e.-cb.  But  ll  e  rro^^t  certain  wa\  i*  \o  .-],(( jfy  the 
number  of  shillings  or  livret-,  instead  of  dollars;  thus  A  -til;  (■  V  i-  \  ;,r- 
rel  of  flour,  at  9$>  shiiJhig-  or  livret ;  in  pa^n  er.t  B  m.ay  iij;(r>.  1  h.  H 
dollars  at  9  ^hi]lir;^=f-  c;  ch,  or  :2  dollars  at  S**.  ?ri.  each,  tiihe.  Leing^ 
equal  to  99  shillings  or  livrcs,  the  sum  tpeciiiedb^  their  aj^reement. 


FRENCH  WEST-INDIES. 

Accounts  are  kept  in  Livres^  Sols  and  Deniers. 
1^^  (K-^niers         -         make         -  1  ?oh 

20  sols  -         -         -         -  1  in  re. 

The  Spanish  dollar  passes  jn  some  places  for  8  livres 
sols,  and  in  olber<  for  9  livres. 


EXCLIAi^GE.  195 

'      1  cwt.  or  1 1 2  lb.  in  the  U.  States  U  equril  to  104  lb.  French. 

100  lb.  French  are  equ.il  to  108  lb.  nearly  in  the  U.  States. 

When  any  commodity  is  to  be  marked  in  French  weifj^ht, 
4  per  cent,  is  added  to  the  neat  hundreds;  thus  a  hoo-shcad 
of  iish  wei^hin^  neat  10  cwt.  is  marked  10  JO  lb.  Fish  ship- 
ped from  the  United  Siate«5  will  answer  to  the  weight  thus 
marked,  provided  it  comes  out  in  g^ood  order,  and  the  casJz 
weighs  exactly  the  cusiomary  tare,  which  is  10  percent. 

100  lb.  of  coifee  or  cottoa,  bought  in  the  French  islands, 
will,  or  ou^ht  to,  weigh  108  lb.  (it  will  often  weig-h  I  10  lb.) 
in  the  United  States  ;  and  as  these  articles  are  sold  here  per 
lb.  there  is  a  gain  of  8  to  10  per  cent,  in  the  weight.  But 
on  sugar,  which  is  bought  per  100  lb.  and  sold  here  per  1 12, 
there  is  a  loss  of  tj  per  cent,  because  there  is  4  per  cent, 
between  the  American  cwt.  and  100  lb.  French,  and  2  per 
cent,  difference  in  the  tare.  The  tare  on  brown  sugar  in  the 
French  islands  being  10  per  cent,  and  the  American  tare 
12  per  cwt.  The  loss  on  clayed  sugar  is  greater,  occasioned 
by  the  customary  tare,  which  is  but  7  per  cent,  in  the 
French  islands,  whereas  it  is  here  12  per  cont.  the  same  as 
on  brown  surar. 

Note.  The  tare  allowed  on  «ugar  among  merchants  is  12  per  112^; 
that  allowed  by  the  custom-house  is  j2  per  100. 

{See  Tare  and  Tret,  page  84.) 

EXAMPLES. 

1.  Change  10692  livres  to  dollars,  at  8}  livres  per  dolLfr. 
^     10692 
4  4 


33)     42768(1290 
33 

97 
66 


316 

297  V 


198 

^98  Ans.  1296  dolk 


19^  'EXCHANGE, 

2.  Change  7713  lirres  to  dollars,  at  9  livres  per  dollar. 

9)7713 

Ans.  857  dollars. 

3.  In  1296  dollars,  at  Fi  livres  each,  how  many  livres! 

1296 

10368 
324 

Ans.    10692  livres. 

4^  857  dollars,  ati^  livres  each,  how  many  livres? 
857 
9 

Ans.  7713  livres. 

5.    What  will  1642  lb.  of  coffee  came  to  at  15  sols  per  Ykt 
1642 
15 

8^10 

1642 


2!0)2 463|0  sols. 

livres     1231    10     Ans.  1231  livres  10  sols. 

6.  1780  lb.  cotton  at  157  Uvres  10  sols  per  iOO  lb.?     ^^ 
1780 
157 

1246a 
8900 

nbo 

10  fols  J         890 

liv.  28U3I50 
^^0 


sols.  lOi'JO  Ads.  2803  liv.  10  sols. 


EXCHANGE  197 

7.  24  barrels  of  beef  at  101  liv.  1  sol,  3  den.  per  barrel? 
liv.     s.     d, 
lUl      1     3 
6 


606     7     6 
4 


"  <2J42o    10     0      Ans.  2 125  liv.  10  sols.- 

8.  How  many  dollars,  at  8  livres  5  sols  per  dollar,  will 
pay  ior  12  hhis.  of  brown  sugar,  weighing  1330 5  Vix  at  4§ 
hvres  per  100  lb.  ? 

13365 
40 


5346,00 
4 


33    )    21384(648 
198 

158 
132 


264 

264  Ans.  648  dolls. 

9.  A  cargo,  amounting  to  12536  dolls,  in  the  United  Stales, 
is  sold  at  12^  per  cent,  advance  on  the  invoice  :  how  manyi 
livres  will  it  amount  to,  estimating  the  dollar  at  Q^  livres  each  I 
12^=1)12536  invoice. 
1567  advance. 


14103  amount. 
8 


1 12824  livres  at  8  per  dollar, 
sols  1         3525J 

Ans.  11 6349 J  livres  at  8^  per  dollar. 

S2 


198 

EXCHANGE. 

10. 

6  hhds.  coffee,  wt.       4471  lb. 

at  14     6  per  lb. 

3^41 

9 

e 

11. 

14  do.  mgr,      do.     16477     - 

38  iiv.  per  100 

6261 

6 

2 

12. 

1  bale  CO   on,  do.          227     - 

150             do. 

340 

10 

0 

13. 

94  hhda.  ii.h,      do.   i0:3i3     - 

33             do. 

33433 

5 

9 

14. 

16  casks,  rice,     do.        6575     . 

40  10       do. 

2662 

17 

6 

15. 

1390  Loops,      .... 

460  per  M. 

667 

4 

0 

16. 

15059  leet  of  boards, 

100         do. 

1505 

18 

0 

17. 

48  shaken  iiiids.  with  heads,     - 

7   15  per  hhd. 

372 

0 

0 

18. 

29  barrels  of  beef,  - 

90   15  perbbl. 

2631 

15 

0 

19. 

6759  velts  of  molasses. 

26  per  velt 

8786 

14 

0 

20. 

32070  galls,  do.  at  73/.  7s.  9d.  per  t 

jerce  of  60  galls. 

39969 

9 

19 

SPANISH  WEST-INDIES. 

Accounts  are  kept  in  Havana^  Laguircu  Fera  Cruz^  ^c.  in  DoU 
Ian  and  ReaU^  reckoning  b  reala  to  a  dollar. 

The  Spanish  arobe  is  26  lbs. 

EXAMPLES.  ^ 

1.  What  will  123  pieces  bretagnes  come  to  at  2G  reals 
per  piece  I 

123 
26 

738  V 

246 

8)3198 


399  6  Ans.  399  dolls.  ^  reali?. 

f:  21784  feet  boards,  at  45  dollars  per  thousand? 
21784 

45  per  M. 

108920 
87136 

08U1280 
8 


3«.«40        Ans.  980  dollr.  2  real? 


EXCHANGE.  l^B 


3.  153  cases  of  gin,  at  8|  doUars  per  case. 
\h3 


1221 

4 

rpals 

16 

4 

2 

do. 

33 

2 

13.38  6       Ans.  1338  dolls.  6  reals. 

"i 

4.  What  is  the  commission  oa  14792  doijars  5  reals  at  4 
per  cent.  ? 

14792  5 
4 


591|70 
8 


5l64         Ans.  591  dolls.  5  reals. 

5.  What  will  42  bbls.  of  white  susfar  come  to,  we>j:hing 
gross  4io  a  robes  18  lb. ;  tare  and  tret  on  the  whole  850  lb? 
at  26  reals  per  arobe  ?     ar.     lb, 
415     18 
858  lb.  make     34       8 


381     10 

26 


2286 
!Q  lb.=a  arobe      10 

8)9916  reals. 

1239  4  Aiis.  lC39dolls.  4  reals. 

dlh,  rh^ 

6.  125  pieces  brctagnes  at  2G  reals     -     •    -    4('6  2 

7.  500  do.  do.    -     -       241  do.       -     .     -  1551    2 

8.  80  umbrellas      -     -  Qi  dollars     -     -     520  0 

9.  1  17  arobes  of  butter  25' do.  per  100  lb.  918  0 
10.  2405  arobes  of  l9ib.S!i;T;ar  25  renls  pr.  arobe  7'»18  0 
llf  Kveodo^.  "1215.  do.  21  do.  i]o.  4358  7 
12.  166D5  fe<it  boards     -     -     4U  (.'oi!'.«  per  M.       607  ^^ 


«0i  EXCH-\NGR. 

EAST-INDIES. 
CALCUTTA, 

Accounts  are  kept  in  Rupees^  Annas  and  Pice. 

12  pifu;  mike  I  anna,  IG  aiiiifis  1  rupee. 

l)v  ia-  Oa2i!(\  or  inarket  exchaii^t*,  for  June,   1797,  the 
exchaii;^e  wa«^,  viz. 

lOU  Eris^lnh  guineas  were  equal  to  9hi]  rnpoes  1  annas. 

lU')  >|>:iiU9b  dollars  were  e<jn:il  to  ^12  rupees. 

in  vveig'his — 16  cb.ttack.!*  make  1  j^eer,  40  seers  1    maud. 
'1  iie  inrlory  maud  is  7b  ib.  English. 
The  b<izar  maud  is     84  lb.  ditto. 
The  ini  ports  jr^esoldby  t  be  f;)ctory  ma\id  and  current  rupees. 
Thi?  exports  are  bougrit  by  the  bazar  maud  and  sicca  rupees. 

100  sicca  ri'.pees  are  equal  to  116  current  rupees. 

Bednah,  tin-plates  and  hides  are  sold  per  coige,  20  to  a 
oorge. 

The  cavid  is  half  a  yard  English. 

EXAMPLE. 

1.  What  will  3905  dry  hides  amount  to  at  12  rupees  per 
corge  ? 

h.  r.  h. 

20     :     12     :  :     3905 
12 


2j0)4686|0 

2343  An?.  2343  rupees. 

2.  How  much  will  189  bazar  mnuds  31  seers  8  chittack^ 
of  sugar  come  to  at  6  rupees  per  maud  ? 
189  31   8 
6 


1134 

20  seers  J 

3 

l'>            i 

1 

8 

1            tV 

0 

2  4 

8  chit,    i 

0 

1   2 

UcJS  11  6    Ans.  1138  r.  11  a.  C  p. 


EXC  RANGE.  201 

BOMDJY. 

Accounts  are  kept  in  Rupees^  Quoriers  and  Ree&. 

100  ree«  mvtke  I  q'lirt  r,  \  qnartcr?  !  rupee. 
218  rupees  were  equal  to  loo  Spariii!*h  dolls,  in  April  1800. 
The  current  money  is  in  Mohnrs,  Rupees  and  Fice. 
60  pice  make  1  rupee,  15  rupees  I  mohur. 
The.  weio^hts  are  pound:^,  mauds  and  candies  ,•    the  pound 
the  same  as  in  English. 
A  Bombay  maud  is  23  lb. 
A  yurat  maud  is  37^  lb. 

21  Surat  maad^s,  of  784  lb.  make  1  Surat  candy. 
Cotton  is  sold  by  the  Surat  candy. 

Camphire  and  Mocha  coffee  are  solcKby  the  Sur:it  maud. 
Jlaiabar  pepper  is  sold  by  the  Bombay  candy  of  5t?8  lb. 

EXAMPLE. 

In  274  bales  of  cotton,  weighing  neat  996  cwt.  2  qrs.  23 
lb.  how  many  Surat  candies? 

764  lb.=7  €wt.         7;996     2     23 

142     200  two  hundreds. 

2i  excess  i^  percent. 
56  two  quarters. 
23 

8U3  Ans.  142  can.  303  Ik 


MjWR^S. 

Jieeounis  are  kept  in  Pagodas^  Fanams  and  Cash. 

50  cash  make  1  fanam,  36  fanams  J  pagoda. 

The  Spwuish  dollars  were  in  1798  and '99,  at  165  dollars 
for  lOOstcir  pHgodaf^ ;   making  the  pagoda  worifi  16.^  cenl6. 

The  rt* venue  laws  of  the    United  States    roxkon  them  at 
181  ceii^s. 

Vhr  i-;'  r:  il.  i)r  <\(]C.\  ^rww)  rupno  is  worlh  46  to  47  els. 
The  rcveuae  uuva  oi  iho  U.  ;:?tatei>  value  thtj;^  ai  50  cents. 


P 


202  EXCHANGE. 

The  current  exchange  is  34U  sicca  rupees  for  100  star 
pf^gcdas. 

A  lack  of  rr.poes  is  1 00,000. 

Cowries  -ive.  sea  shells  us^ed  as  small  money  in  India  and 
on  the  coast  of  Africa,  to  make  ch.tuge  among*  ihe  natives  in 
the  bazur  or  m:^rket,  and  in  payment  to  the  cooties  or  la- 
bourers. In  May,  17^2,  a  rupee  vxa?  north  5120  cowries. 
The  common  cowries  are  generally  at  5  to  7  rupees  \u\v 
bazar  maud,  the  b-tter  sori  f n  m  10  to  14  rupees  per  maud, 
the  pr'ce  vary  ns;  acconhng  to  the  kind. 

I'he  picul  is  153^  lb.  Ersglish. 

lOu  c  Utiis  mi^ke  a  picul. 

A  maud  is  251  h.  troy  :  20  mauds  make  1  candy. 

The  excejUi'J34^^^i'  their  cloth  is  delined  by  the  threads  in 
the  warp. 

The  duty  payable  at  the  custom-house  is  2^  per  cent, 
outwards  and  inwards,  '^rhis  is  taken  on  imports  according 
to  the  invoice,  and  on  exports  at  the  actual  cost  at  ihe  bazar 
er  market. 


BAT  AVI  A. 

Accounts  are  kept  in  Rix  Dollars  and  Stivers. 

The  rix  dollar  is  48  stivers. 

The  ducatoon  is  80  ditto. 

The  Spanish  dollar  is  64  ditto ;  fiometime?  it  passes  at  60  st. 

125  lb.  Dutch  are  equal  to  K3  J^  lb.  English. 

\'?b  do.     ^     make     -     1  picul. 

100  cattas         -       -        1  ditto. 

EXAMPLES. 

1.  In  1333  rix  dollars  16  stivers,  bow  many  ducatoons  ? 
1333  16 
48 

10670 
5333 


810)640010 
Ans.  800  ducatooDS. 


EXCHANGE.  203 


2.  What 
dollars  per  jj 

will  127477  cattas  of  bar 
iicul  ? 

ircn 

come 

to  at 

9 

fix 

As 

cat. 
luO 

rd. 
:     9     : 

cat. 
9 

^ 

U  472,93 
48 

744 

372 

29^0  24 


44,t)i     Ans.  11472  r.  dolls.  44  st. 

3    What  will   3894  bottles  of  wine  eome  to  at   36  stivers 
per  bottle  ? 

3894  Or  thut?,     3'5  Miv.=f  rix  doll. 

3894 

24  stiv.   I-      1947                                          3 
I        97;^  24  

4}i]c.a2 

2^)2t)  24 
An?.  2920  rix  dolls.  24  stiv. 

4.  In  31478  lb.  of  sun^ar,  how  many  piculs? 
12o)31478(25l 
20O 

647 
625 

228 
125 

103         Ans.  251  picii^s,  103  lb. 

5.  In  50r)32  lb.  how  many  plculs  ?  An.^.  405     7 

6.  in  l^o48 101   rj 


204  EXCHANGE. 

7.  AVhat  will  279  piculs  26  il>.  oi' feugar com^  to  at  7-J  rix 
doiiar^  per  picul  ?  279 

H 

1953 
K39  n 

25=1  1    '24: 


2094  OO     .     An5.  2094  rix  dolls. 

CIJLVA 
9iilcukiiion9  arc  made  in  7(//e,  Alace^  Canr^oreens  and  Cash* 
JO  citsli  -  mnke         *  1  cahdareen. 

10  c.mflareens  tw       ^         _      j  mace. 

10  mace  -  '•  -  1  tale. 

Th<»  tn'.e  oi"  China  is  optima  ed  at  1  dollar  48  cents  in  the 
Up'ttd  Stati-s. 

The  Spanish  dollar  i*  current  a1  72  candareens 
Weights  are  in  'i'ale.s,  Ficuls  and  Cattas  5   16  tales  make  I 
e^d'ia  ;    100  catla?  1  picui. 

A  picul  i?*  eipial  to  \:yd^  \h    Ensrlis^h. 

The  cav  d  o\  China  is  l4/|f  inches:  it  is  divided  into  10 
parts. 

To  change  English  Ptmnds  to  dtitas. 
Rule.     Ded»?ct  lb  per  cef)t.  or  one  quarter,  lor  cattas. 

F.XAMTME. 

In  C2668  lb.  English,  he^v  many  cattas  ? 

15t67 

Ans    47001  caftns. 
To  change  Cattas  to  Fo^/nds  English. 
Ilrr.r.  Add  one  third  Ibr  pounds  English. 

FXAVri  F.. 

Fn  47001  cattas  how  manj  lb.  English? 
^)47()0} 
156G7 


Ans.  G2GG3  lb.  English. 


EXCHANGE.  205 

PRACTICAL  qUESTIO.JVS, 

1.  Wliat  is  the  amount  of  308  chests  of  bohea  tea,  weighing 
Tieat  101956   lb.  at  15  tales  per  picul? 
1)101956  lb. 
25489 

cat.         tal. 

100    :     15  ::      76467  cattas. 
15 


382335 
7G467 


1 1470,05         Ans.    1 1470  tales  5  can'd. 
2.  What  will  75  chests  of  souchong  tea  come  to,  weighing 
neat  4875  lb.  at  44  tales  per  picui? 
i)4875 
1218| 


36561  cattas. 
44 

14624 
14624 
11 


1608,75         Ans.  1608  tal.  7  mar.  5  cand. 
3.    How  many  dollars   will  pay  for   an   invoice  of  tea., 
amounting  to  6446  tales  1  mace  6  candareens? 
72)6446   1   6(8953 
576 


648 


381 
360 

216 

216       Ans.  8953  dollars. 


^06  EXCHANGE. 

MAJVILLA. 

Accounts  are  kepi  in  Dollars^  Reals  and  Quarics. 
12  qua  (OS  make  1  real,  8  reals  1  dollar. 
The  arobe  is  ,:5  ib.     5J  arobes  make  1  picul. 
Their  lOOlb.  is  equ.il  to  104  lb.  English. 

EXAMPLE. 

1.  What    will    1^97  bags  of  sugar  amount  to^    weighing 
neat  1^61  piculs  1  arobe  I74r  lb.  at  6  dollars  per  picul? 
1361    1    171 
6 


1  ar. 
121  lb. 


8167     6   10 

Ans.  8167  doll?.  6  r.  10  q. 
pic.  ar.  lb.     dlls  re. 

2.  118  bags  of  sugar,  weighing  89   1   22i   at  5  7 

Ans.  524  dolls.  7  reals. 
^  pic.  ar.  lb.     dlls. 

3.  663  bags  of  sugar,  weighing  469  3  18  at  6 

Ans.  2819  dolls. 


8166 

fr          1 

0     8J 

i 

4     4J- 

i 

1      9 

*  COLUMBO,  ISLE  OF  CEYLOJV. 

The  money  is  in  Poper^  Silver  and  Gold, 

Paper  money  is  in  the  bills  of  the  Company,  and  is  of  un- 
certain value. 

Silver  is  in  the  rupees  of  different  parts  of  India. 

The  sicca  rupee  is  worth  more  than  any  other  by  7  to  8 
per  cent. 

Gold  is  the  mohur  pagoda. 

The  exchange  is  various,  as  silver  is  rarely  Feen. 

6  stivers  make  1  shilling  Flemish. 

0  shillings         -         -  -  1  rix  dollar. 

::0  stivers     -         -         -         -      1  rupee. 

G  U-    do.  -         -         -  1  Spanish  dollar. 


EXCHANGE. 


207 


JAPAN. 

Accounts  are  kept  in  Tales^  Mace  and  Candareens. 

10  candareens  make  I  mace. 

10  miice  -  1  tale  =  f  of  a  dollar,  or  75  cents. 

lU  mace  are  equal  to  1  rix  dollar. 

6  taies  make  a  corban,  a  gold  coin  not  used  in  accounts. 

In  weights — 10  tales  m\ke  I  mace,  16  maces  1  catta. 

The  ich m,  or  hickey,  is  3i  feet. 

The  balee  is  65  quarts. 

35  per  cent,  was  the  duty  on  privileged  imports  in  1799.  It  ts  on 
exports  (which  are  all  free  of  daty)  that  the  Du'ch  make  their  profit  on 
their  return  to  Batayia.  A  privilege  is  granted  to  the  captains  of  the 
Dutch  ships  to  carry  money,  which  often  sells  at  an  advance. 

EXAMPLE. 

How  much  is  the  neat  proceeds  of  4  silver  watches,  at  35 
tales  each,  deducting  the  duty  of  35  per  cent   ? 
35  tales 
4 


140 
35  per  cent. 


700 
420 


Sale  140 
Duty   49 


4J,00        Ans.  Neat  proceeds  91  tales. 


FORM  OF  AN  ACCOUNT  OF  SALES. 


4  silver  watches,  1st  kind 
6  «,lver  watches,  2d  kind 


tales. 

35 

23,1 


Duties. 

tales. 
49 
48,5,1 


iNeat. 

tales. 
91 
90,0,9 


The  article  is  given  in  the  first  column,  the  price  in  the 
next  column,  the  duties  in  the  third,  and  the  neat  proceeds 
in  the  fourth. 


.208 


EXCHANGE. 


PARTICULARS 

Of  the  ToNxVAGE  of  Goods,  as  calculated  to  make  up  the  Ton- 
nage for  the  Freight  of  Goods^  brought  in  East-India  or 
China  ships  to  Europe- — viz; 

PIECE  GOODS. 


Fort  St. 

George. 

Bengal. 

Pieces  to 

Pieces  to 

the  ton- 

the  ton. 

Allejars 

- 

800 

Elatches 

-      R.SOO 

Betelles     - 

- 

-     400 

Emmertiea 

-      600 

Callawapores 

■- 

800 

Gurrahs 

400 

Chintz  of  all  sorts 

- 

K;400 

Ditto,  long 

-      200 

Ginghams 

. 

800 

Ginghams,  coloured 

600 

Izzares 

- 

-      800 

Humhums 

-      400 

Longcloths     - 

- 

160 

Habassies 

600 

Moorees    - 

- 

-     800 

Humhums,  quilted 

-       100 

Sallampores    - 

- 

400 

Jamdannies 

800 

Sastracundies 

- 

-     800 

Jamwars 

-       600 

Bengal. 

Laccowries  - 

600 

Addaties 

- 

700 

Lungees  Herba 

-       800 

Alliballies 

- 

-     400 

Mulmuls 

400 

All  a  chaws 

. 

1200 

Ditto  handkerchiefs    - 

-       400 

Allibannies 

. 

R.800 

Mahamodietes 

400 

Arras      - 

_ 

-     R.400 

Mamodies 

-  R.400 

Atchabannies     - 

. 

-      800 

Nillaes 

800 

Baftaes 

. 

-      R400 

Nainsooks 

-        400 

Ba.idannoes,  or  Taffa  de 

Peniasoces 

800 

Foolas     - 

_ 

-       R.800 

Photaes 

R.SOO 

Carridanies 

- 

-       600 

Pcrcaulas      - 

800 

Callipatties 

. 

400 

Putcahs 

R.400 

Coopees 

_ 

600 

Romans 

-       R.800 

Calicoes 

. 

400 

Sannoes 

400 

Chillaes 

» 

600     Seerbetties 

400. 

Chowtars 

. 

600     Seerbands 

600 

Cimndeibannies 

_ 

800  i  Seersuckers 

600 

Chinitachures 

_ 

R.SOO  1  Seerhaudconnaes 

400 

CambMcs 

- 

R.400     Seershauds 

R.400 

CTiucklaes    - 

> 

400     Seerbafts 

400 

Cushtaes 

_ 

800     Shaulbafts 

400 

Cossaes 

- 

400     Succalcons 

R.800 

Charconnaes     - 

. 

600     Sooseys 

400 

Cuttannaes 

- 

R.SOO  ;  Sorts       - 

400 

Doosoqties 

_ 

-    R.400  \  Terridams 

400 

Dun^^aries 

- 

R.400  '  Taffeties  of  all  sorts 

R.800 

iloreas     - 

. 

400  1  Tanjeebs. 

400 

Dimities 

- 

600  ';  Tepoys       - 

R.SOO 

Diapers,  broad 

-      400  1  Tainsooks 

•     400 

l^iUo,  narrow 

- 

«00 

1 

EXCHANGE. 


PIECE 


209 


Bombay. 


Annabatches 

Bombay  stuflfs 

Bvrampauts 

Bejuiapauts     - 

Boralchawders,  or  brawls 

BefeHees 

(Jhelloes 

Chintz  of  all  sorts 

Dooties      -        -         - 

Guinea  StufFw,  large 

Ditto,  small 

Loiigcloths,  whole  pieces 

Difto,  half  do. 

Lemanees 

PJusters         -         -         - 

Nunsarees 

Nej^enepauts 

!Nicanees,  large 

Diito,  small 

S'llampores 

S-uiFh,  brown 

Tapseils,  large 

Diuo,  small 


Pieces  to 
tlie  to?i. 
R400 

-  R400 
400 

-  R.400 
1200 

400 
R.400 
1^400 
R  400 

600 

-  1200 

leo 

320 

R.800 

400 

R.400 

400 

.       600 

600 

-      400 

R.,10f> 

-  4C0 
6C0 


W 


'  Arrangoes 
Aiocs  •♦ 

Benjamin 
Borax 

Cardemons,  fine  good^ 
Cakelack 
Carmen i a  \^'ool 
Cambo*(ium 
Ca«sia  JJgnea 
Ca.-,i  •  buds 
Camphire 

Co   Oil  yarn,  fine  goods 
Co.vie^-,  gruff  do. 

(  olT»  e,  fine    do. 

Ciz.jiaber 
Cloves 

Dra^Oii's  Blood 
Gum  Arabic 

Elcmi 

AmiTiO-iiacum 


EIGHABI 
Cwt  to 
the  ton, 
20 
16 
20 
20 
12 
16 
10 
20 

-  8 
12 

-  vl.3 

10 
20 
18 
10 

-  J2 
20 

-  3  6 
16 
16 

T 


GOODS. 

China. 

i-W  ,";'.';  it) 
the  ton. 

Nankeen  cloth       -         -       R.100 
Silks,  of  all  roris         -  R.SOO 

China  ware,  50  cubical  feet  ^o  :hs 
ton,  or   about  4    chests  of   iLe 
usual  dimensions. 
Other  meae^urable  good^,  50   cubi- 
cal feel  to  the  'on. 

N.  B.  Where  the  letter  R  is 
set  against  pieces  of  400  .o  the 
ton,  it  shows  tho'.e  goods  are  to  .  e 
reduced,  or  brought  ;o  a  standard 
of  •  6  yards  long  aid  ;  b' o.^d. 

Where  against  pieces  800  to  the 
ton,  to  iO  yards  long  ai-^d  i  Lroud. 

EXAJMPI.E. 

1000  pieces,  of  12  atd-  long  and 
1  1-8  broad,  at  4(}0  to  'he'  lo., 
make  844  piece-,  or  2  tons  44 
pieces. 

1000  piece-  of  0^  Tard.s  long  and 
1  1-S  bro  d,  at  800  to  .he  ton, 
is  J 181  pieces,  or  1  ton  SSI 
pieces. 

LE  GOODS, 


Cidt.  to 

the  ton. 

Gum  Opoponax 

Sagape.'iUm     ♦ 
Saroocol 

IS 

Indigo 

lion  Kintlage 

12 

20 

Musk 

20 

Myrrh 

^?OTher  of  Pearl  Shells 

16 
20 

Nux  Vomica 

15 

Pepper 
Quicksilver 

20 

Rhubarb 

S 

Raw  Silk 

10 

Ditto  in  chests 

s 

Dii»o  in  bales  or  bujidles 

10 

Redwood 

20 

Rice 

.       20 

Shellac 

16 

Secdlac         .              , 

.       18 

Siickbck 

le 

210  ARDITR\TION  OF  EXCriANGE. 

WEIGH  ABLE  GOODS. 


Cwt.  to 

the  ton. 
Saltpetre  .  .  20 


Cwt  to 

the  ton. 
Tea,  Green  .  .  S 


Seaaa           .              ,             .  8  ;            Boiiea      .             .                 10 

Sa<;o        .             .              .  16  i  Arrack         Gauge  gallons          251 

Diito,  packed  in  china  ware  -  -  !  Canes         .             .            Tale  300 

Tu'eiia/;ue           .              .  20  .  Wangliees  and  Bamboos           3000 

Turmeric       ,              .            .  IG     Rattans  equal  to  16  cwt.           6000 

Tiiical       .         .             -  16 


ARBITRATION  OF  EXCHANGE. 

When  the  rates  of  exchange  between  several  cntrritries  in 
succession  are  given,  to  find  the  rate  of  exchange  between 
the  first  and  last  place  in  the  correspondence, 

Rule.  Find  by  proportion  the  value  of  the  sum  originally 
remitted  in  the  different  moneys  of  the  coimlrios  through 
which  it -passes,  according  to  the  rates  of  the  different  ex- 
changes, and  so  proceed  till  the  whole  is  finished.     Or, 

Multiply  all  the  first  terms  of  the  different  statings  toge- 
rber  for  a  divisor,  and  the  second  terms,  together  with  the 
S'lm  remitted,  for  a  dividend,  and  the  quotient  is  the  amount 
received  in  the  denomination  of  the  last  place  m  the  corre- 
spondence :  from  this  result  the  rate  of  exchange  is  readily 
foupd  by  proportion. 

fxampi.es. 
1.  A  merchant  in  London  has  credit  for  500  piastres  in 
Leghorn,  tor  which  hti  can  draw  directly  at  52r/.  sterling  per 
piastre,  but  choosing  to  have  it  remittetl  by  a  circular  route, 
they  are  sent  by  his  order  to  Venice,  at  95  piastres  for  lUO 
ducats  banco;  from  thence  to  Cadiz  at  350  maravadies  per 
(3k  It  banco;  from  thence  to  Lisbon  at  t)3()  reas  per  piastre 
o.  2  2  maravadies  ;  from  thence  to  Amsterdam  at  4Sd.  Flem- 
ish for  100  reas;  from  thence  to  Pans  at5Uy.  Flemish  per 
crown  ;  and  from  thence  to  London  at  oOd.  sterling  per  crown. 
What  is  the  arbitr;}ted  price  between  London  and  Leif'iorn 
lev  p.astre,  and  whit  is  gained  or  lost  by  this  circular  remit- 
tal uce,  without  reckoning  expeu'-jci  ? 


AUBiTRATION  OF  EXCflANGE. 


2lt 


yid.-^t. 

d.  ban. 

piast. 

d  6a/j. 

95 

:      100     : 

:          500 

:         o'^i^i^  in  Venice. 

d.b 

mar. 

d!.  6. 

war. 

1 

:     350     : 

:          52G.^, 

:    18i2I()' 

J  in  Cadiz. 

mar. 

rea.^. 

??iar. 

reas. 

270, 

:     t3.V)     : 

:    184i!0;-5 

:  4^2o  ;')4 

in  Lisbon. 

reas. 

d.fl. 

reas. 

^./. 

400 

:         I. J    : 

:    4h>oo4 

:   51  Hitl- 

in Amsterdam. 

d.JI. 
51 

cr. 
:          1     :: 

d.fl 

5.1  '9  J 

er. 

:     945,^ 

in  Par.s. 

cr. 

1 

d.  St. 
.50    : : 

cr. 

£      s. 
:      l.ij    iO 

d. 

!•   sterlinw". 

Or  thus 
piast.     d.b      mar.         reas      d.fl.      cr. 

:j.>  X  -I   X   i7i  X  40U  X    >i  X   »  =  55314400 
piast.      d.  b.      mar.       reas.       d.fl       cr.     d.  st. 
5j^  X  100  X  JfoO  X  ^^^^)  X  4<3  X  I  X  00=1587600000000 


558 1 4  ]|  JO)  1  587600000  j 

.>0(12)2844i| 

lllBi^BB 

2iu;.^s7iO    i\ 

47l.3li0 

jbn8   iO  4]-  as  above. 

2nHG80 
2232576 

*i  1710  10 
2232576 

2:^84^i40 

2232576 

152064 

4 

piiut.     £,,     s.     d,     piast,  d. 
500  :    118   10  4|  :  :    1    :  56||JJ 

553144)boa25b^ 
5=)B14  4 

1 
f 

50112 
AmoTint  received  by  circular  remittance 
600  piastres  at  b2d 

C  Gained  by  circui  r  re  •  ittiince 
Ans.   / 

(  Arb.lmteJ  value  of  a  p.actrc  by  do. 


£ 

s. 

d. 

118 

10 

H 

108 

G 

8 

£10 

3 

^} 

bmud.st. 


^12  AMERICAN  DUTIES. 

2  A  merchant  in  Bosion  has  £'ii'ib  sterling  in  LonHoD, 
wh  ch  he  can  draw  lor  at  ok/,  sterling  per  dollar,  but  choos- 
ing to  try  a  circular  route,  it  is  sent  to  Dublin  at  £lO()  ster- 
ling for  £l09  Irish  ;  thence  to  Hamburgh  at  12-J  marks  bni> 
CO  per  pound  Irish  ;  thence  to  Amsterdam  at  ;53  florins  for 
40  marks  banco  ;  thence  to  Copenhagen  at  5  florins  for  2 
rix  dollars  of  Denmark;  thence  to  Bremen  at  3  marks  per 
rix  dollar  of  Denmark  ;  thence  to  Russia  at  5  marks  for  2 
rubles;  thence  to  Bordeaux  at  5  francs  per  ruble ;  thence 
to  Cadiz  at  18  reals  plate  for  10  francs ;  thence  to  Lisbon  at 
li'50  reals  plate  for  100  roillreas;  thence  to  Leghorn  at  760 
soldi  for  88  millreas ;  thence  to  Smyrna  at  2  soldi  per  pias- 
tre ;  thence  to  Jamaica  at  24^^.  Jamaica  currency  per  pias-v 
tre  ;  and  thence  to  Boston  at  OOri.  Jamaica  currency  per 
dollar  :  what  is  gained  or  lost  by  this  circular  remittance  ? 

Ans.   117  dolls.  42  cts.  gained. 


AMERICAN  DUTIES 

ARE    CALCULATED    AS    IN    THE    FOLLOWLN*- 
EXAMPLES. 

1.  What  is  the  duty  on  2885  gallons  of  molasses,  at  5  ctSy 
per  gallon  ? 

2885 
5 


14i25  cents.  Ans.   144  dolls   25  ct^. 

?.  What  is  the  duty  on  the  above  molasses,  if  imported  in 
n  ft']  ei^a  vessel,  the  rate  being  5]  cts.  per  gallon,  or  10  per 
c^iit,  more  than  m  an  American  vessel? 

^^85  Or,     14  1,25  as  above. 

5,^  U)  per  cent.        W^i'i'j 


llMb  dolls.    158,G7J- 

1  '.\'li 

ioUs,   Ibl'fil^.  An?.  158  dolls.  67J  ct8K 


AMERICAN  DUTIES.                        213 

3.  How  much  is  the  duty  on  3720  gallons  of  gin,  at  3ij;\ 
cents  per  giiilon  ? 

3720  3720 

31tV  9 


3720  10)33480 

11160  

3348  3348 


dolls. cts. 

^ns.  33 

19 

34 

84^ 

-      80 

43 

99 

Hi 

845 

55 

dolls.     l;186,6a'  Ans.  1186  dolls.  68  cents. 

4.  1273  lb.  chocolate  at  3  cents 

5.  965  lb.  do.  in  a  foreign  vessel,  at  Sy'g  do. 

6.  1149  lb.  cheese,  at  7  do. 

7.  J  295  lb.  do.  in  a  foreign  vessel,  at  1-^^  do. 

8.  1879  galls.  Champaigne  wine,  at  45  do. 

9.  2675  do.  London  particular  Madeira,  at  58  do.    1551   50 

10.  What  is  the  duty  on  53  cwt.  2  qrs.  21  lb.  of  untarred 
cordage,  at  225  cts.  per  cwt.  ? 
225 
5;i 

675 
1125 
2  qrs.     i  112J 

14  lb.     1  23 

7    do.     i  14 


120,79-J-  Ans.   120  dolls.  79^  cts. 

11.  What  is  the  duty  on  the  above  cordage  in  a  foreiga 
vessel,  at  247^  cts.  per  cwt.?  Ans.  13i  dolls.  87i  cts. 


214  AMERICAN  DUTIES. 

12.  How  much  is  tho  duty  on  4  hhds.  of  brown  su^far,  wt. 
gross  30  cwt.  3  qrs.  19  lb.,  tare  12  lb.  per  100,  at  2^  cts. 
per  lb.? 

3800 
456=excess  12  per  cent. 
84 
19 


gross 
tare 

4359 
523 

3836 
2J 

4359 
12 

623,08 

7672 
1918 

95,90  Ans.  95  dolls.  90  cts. 

13.  What  is  the  duty  on  this  sugar  in  a  foreign  vessel,  at' 
^  cents  per  lb.  ?  Ans.  105  dolls.  49  cts. 


The  modes  of  estimating  ad  valorem  rates  of  duty. 

The  advalorem  rates  of  duty  upon  goods,  wares  and  mer- 
chandises, at  the  place  of  importation,  shall  be  estimated  by 
adiiing  20  per  cent,  to  the  actual  cost  thereof,  if  imported 
from  the  Cape  of  Good  Hope,  or  from  any  other  place  be- 
yond the  same,  and  10  per  cent,  on  ibe  actual  cost  thereof, 
if  imported  from  any  other  place  or  country,  including  all 
charge!* ;  commiJisions,  outside  packages  and  insurance  ex- 
cepted.—  [See  Laws  oj  iht  United  States.) 


AMERICAN  DUTIES.  215 


EXAMI^LES. 


1.  What  is  the   duty  on  an    invoice   of  silver   and   plated 
ware,  imported  from  London,  the  cost,  exclusive  of  commis- 
sions, kc.  being  £359  1(5  4,  at  15  per  cent,  ad  valorem? 
359 
444  cent5  per  jj  sterling. 


105. 

5*. 

35.  4d. 


1436 

1436 

1436 

i 

?22 

i 

111 

i 

74 

actual  cost     159H03  cents. 
10  per  cent,  added       1590O 


175783 


lOJ-,.  ,17578 

6^  8789 

for  15  percent.  2G3G7  cts.   Ans.  eBf5  dolls.  67  cts. 

2.   What  vv'll  it  amount  to  in  a  fore'*2:n  v»>*i?oi,  at  16^  per 
cent,  ad  valorem?  Ans.  2\j\J  duils.  4  cent*. 


TJie  rates  at  which  all  foreign  coins  avd  currencies  are  estima' 
ted  at  ike  Custom-Houses  oj^ the  United  Slates. 

dolls,  cts. 
Each  pound  sterling  of  Great  Britain,  at      - 
Each  pound  sterling  ot  Ireland        -         -         - 
Each  livre  tournoisJ  of  France     -         -         -         - 
Each  florin  or  guilder  of  the  United  Netherlands 
Each  mark  banco  of  Hamlnirgh       -         -         - 
Each  rix  dollar  of  ])onm:irit        -         .         .         - 
Each  real  of  plate  of  Sp.iin       -       -         -         - 
Each  real  of  vellon  of  Spain        -         -         -         - 
larh  miliree  of  Portugal         -         .         -         - 

Each  tale  of  China 

Each  pa4^oda  of  India      -         -  .         -         . 

Each  rupee  of  Bengal         •         -         .         -         - 


4 

44 

4 

10 

I8i 

40 

33  L 

1 

10 

5 

1 

24 

1 

43 

I 

84 

50 

216  PROGRESSION. 

PROGRESSION 

Consists  of  two  parts — Arithmetical  and  Geometrical. 


ARITHMETICAL  PROGRESSIOJST 

Is  when  a  rank  of  numbers  increases  or  decreases  regu- 
larly, by  the  continual  adding  or  subtracting  of  some  equal 
number:  As  1,  ^2,  3,  4,  5,  6,  are  in  arithmetical  progression 
by  the  continual  increasing- or  adding  of  one  5  and  1 1,  9,  7,  5, 
3,  I,  by  the  continual  decrease  or  subtraction  of  two. 

JVoTE.  When  any  even  number  of  terms  dilTer  by  arith- 
metical prog-ression,  the  sura  of  the  two  extremes  will  be 
equal  to  tbe  two  middle  numbers,  or  any  two  means  equally 
distant  from  the  extrt'mes  :  As  2,  4,  G,  8,  10,  12,  where 
C-l-8,  the  two  middle  numbers,  are  =:^  12-f-2,  the  two  ex- 
tremes, and  =r)0-f  4,  tbe  two  means,  =  14. 

When  the  number  of  terms  are  odd,  the  double  of  the 
middle  term  will  be  equal  to  the  two  extremes,  or  of  any 
two  means  equally  distant  from  the  middle  term:  As  I,  2, 
3,  4,  5,  where  the  double  of  3=54.1c=:2-f  4=6. 

In  arithmetical  progression  five  things  are  to  be  observ- 
ed, VIZ.  J.     The  first  term. 

2.  The  last  term. 

3.  The  number  of  terms. 

4.  The  equal  difference. 

5.  The  sum  ot  all  the  terms. 

Any  three  of  which  being  given,  the  other  two  may  be  found. 


The  firsts  second  and  third  terms  given^  to  find  the  fifth. 
Rule.     Multiply  the  sum  of  the  two  extremes  by  half  the 
number  of  terms,    or  multiply  half  the  sum  of  tbe  two  ex- 
tremes  by  the  whole  number  of  terms,    the  product  is  thi3 
tatal  of  all  the  terms. 


EXAMPLES. 


1.  How^  many  strokes  does  the  hammer  of  a  clock  strike 
in  12  hours?  12-fl  =  !3,  then  13X6=78.     Ans. 

2.  A  man  buys  17  yards  of  cloth,  and  gives  for  th'G  first  yd. 
2s.  and  for  the  last  10s.  what  do  the  17  yards  amount  to  ? 

Ans.  £5  2s. 


PROGRESSION.  217 

3.  If  100  eggs  were  placed  in  a  right  line,  exactly  a  yard 
asunder  from  one  another,  and  the  first  a  yard  from  a  bas- 
ket, Avhat  length  of  ground  does  that  man  go  who  gathers  up 
these  100  eggs  singly,  returning  with  every  egg  to  the 
basket?  Ans.  5  miles  1300  yards. 


The  fir  st^  second  and  third  terms  givcn^  to  find  the  fourth. 

Rule.  From  the  second  subtract  the  first,  the  remainder 
divided  by  the  third  less  one  gives  the  I'ourth. 

EXAMPLES. 

1 .  A  man  had  8  sons  ;  the  youngest  was  4  years  old,  and 
the  eldest  32  ;  they  increase  in  arithmetical  progression  : 
what  was  the  common  difference  of  their  a«es?  Ans  4. 

32—4=28  then  28  —  8—1=4  the  common  difference. 

2.  A  man  is  to  travel  from  Boston  to  a  certain  place  in  12 
days,  and  to  go  but  3  miles  the  first  day,  increasing  every 
day  by  an  equal  excess,  so  that  the  last  day's  journey  may 
be  58  miles;  what  is  the  daily  increase,  and  how  many 
miles  distant  is  that  place  from  Boston  ? 

Ans.  5  miles  daily  increase. 
Therefore  as  3  miles  is  the  first  day's  journey  ; 
3-f  5=  8  second  ditto, 
84-5=13  third  ditto,  &c. 
The  whole  distance  is  366  miles. 


The  firsts  second  and  fourth' terms  given.,  to  find  the  third. 

Rule.  From  the  second  subtract  the  first,  the  remainder 
divide  by  the  fourth,  and  to  the  quotient  add  1,  gives  the 
third. 

EXAMPLES. 

1.  A  person,  trayelling  into  the  country,  went  3  miles  the 
first  day,  and  increased  every  day  by  5  miles,  till  at  last  ho 
went  58  miles  in  one  day  ;  how  many  days  did  he  travel  ? 

ro     c  ,  ^  Ans.   12. 

58— 3  =  55  then  55-T-5x=li  and  11  +  1=12    the  number  of 
days.  U 


tl8  PROGRESSION. 

2.  A  man,  being  asked  how  mnny  son?  he  had,  said  that 
the  youngest  was  4  years  old  and  the  eldest  32,  and  that  he 
increased  one  in  his  family  every  four  years  ;  how  many 
^'^^^  lie?  .  Ans.  8. 


The  second^  third  and  fourth  giren^  to  find  the  first. 

Rule,  Multiply  the  fourth  by  the  third,  made  less  hy  1^ 
the  product  subtracted  from  the  second  gives  the  first. 

EXAiMI'I.ES. 

L  A  man  in  10  days  went  from  Boston  to  a  certain  town 
in  the  country,  every  day's  journey  increasing  the  former 
by  4,  and  the  hist  day  he  went  was  46  miles  :  what  was  th« 
first?  Ans.   10  miles. 

4x10—1=36  then  46—30=10,  the  first  day's  journey. 

2.  A  man  takes  out  of  his  pocket,  at  8  several  times,  so 
many  different  numbers  of  shillings,  every  one  exceeding  the 
former  by  6  ;  the  last  46  ;  what  was  the  first  ?         Ans.  4. 


The  second^  third  and  fifth  given.,  to  find  the  first. 
Rule.     Divide    the  fifth  by  the  third,   and  from  the  quo- 
tient subtract  half  the  product  of  the  fourth,  multiplied  by 
the  third  less  1,  gives  the  first. 

EXAMPLE. 

A  man  is  to  rpceive  £360  at  12  several  payments,  each 
to  exceed  the  former  by  ,£4,  and  is  willing  to  bestow  the 
first  payment  on  any  one  that  can  tell  him  what  it  is,-  what 
will  that  person  have  for  his  pains  ?  Ans.  £8 

4X1?^ 

3G0-T- 12=30  Ihen  30 =6,  the  first  payment. 


The  firsts  third  and  fu'th  given^  to  find  the  second. 

Rule.  Subtract  the  fourth  from  the  product  of  the  third, 
multiplied  by  the  fourih,  that  remainder  added  to  the  first 
sives  the  second. 


PROGRESSION.  21» 

EXAMPLE. 

What  is  the  last  number  of  an  arithmetical  progression, 
beg^inning  at  6,  and  continuing  by  the  increase  of  8  to  20 
places?  Ads.  158 

20x^—8=152  then  152  +  6=158,  the  last  number. 


GEOMETRICAL  PROGRESSIOJ\' 

Is  the  increasing  or  decreasing  of  any  rank  of  number?  by 
some  common  ratio,  that  is,  by  the  continual  multiplication 
or  division  of  some  equnl  number:  as  2,  4,  3,  IG,  increase 
by  the  multiplier  2,  and  16,  8,  4,  2,  decrease  by  the  divisor  2. 

Note.  When  any  number  of  terms  is  continued  in  geo- 
metrical progression,  the  product  of  the  two  extremes  will 
be  equal  to  any  two  means  equally  distant  from  the  extremes  : 
As  2,  4,  8,  16,  32,  61,  where  64x2=4X32=8x  10=128. 

When  ihe  number  of  terms  are  odd,  the  middle  term  mul- 
tiplied into  itself  will  be  equal  to  the  two  extremes,  or  any 
two  means  equally  distant  from  the  middle:  as  2,  4,  8,  16, 
32,  where  2X32=4X  l6=8Xc'=-64. 

In  geometrical  progression  the  same  five  things  are  to  be 
•bserved  as  in  arithmetical,  viz. 

1.  The  fir>t  term. 

2.  The  last  term. 

3.  The  number  of  terms. 

4.  The  equal  difference,  or  ratio. 

5.  The  sum  of  all  the  terms. 

NoTK.  As  the  last  term  in  a  l^ng  series  of  numbers  is 
very  tedious  to  come  at  by  continual  multiplication  ;  there- 
fore, lor  the  readier  tinding  it  out,  there  is  a  series  of  num- 
bers made  use  of  in  arithmetical  j)roportion,  called  indices, 
beginning  with  an  unit,  whose  common  difference  is  one  ; 
whatever  number  of  indices  yo^  make  use  of,  set  as  many 
numbers  (in  such  geometrical  proportion  as  is  given  in  the 
question)  under  them: 
.     1,2,  3,    4,     5,    6  indices. 

2,  4,  8,  16,  32,  61  numbers  in  geometrical  proportion. 
But  if  the  first  term  in  geometrical  proportion  be  differ- 
ent from  the  ratio,  the  indices  must  begin  with  a  cipher : 
^g  0,  1,  2,  3,    4,     5,    6  indices. 

1,  2,  4,  8,  16,  32,  64  numbers  in  geometrical  proportion. 


£20  PROGRESSION. 

When  the  indices  begin  with  a  cipher,  the  sum  of  the  in- 
dices made  choice  of  must  be  always  one  less  than  the  num- 
ber of  terms  given  in  the  question  ;  for  1  in  the  indices  is 
over  the  second  term,  and  2  over  the  third,  (^-c. 

Add  any  two  of  the  indices    together,  and  that  sum  will 
agree  with  the  product  of  their  respective  terms.  ^ 
As  in  the  first  table  of  indices  2-f    5=     7 
Geometrical  Proportion  4X32=123 

2+   4=^     6 
Then  in  the  second  4X  it)=  64 

In  any  geometrical  progression  proceeding  from  unity,  the 
ratio  being  known,  to  find  any  remote  term,  without  produ- 
cing all  the  intermediate  terms. 

Rule.  Find  what  figures  of  the  indices  added  together 
would  give  the  exponent  of  the  term  wanted,  then  multiply 
the  numbers  standing  under  such  exponent  into  each  other, 
and  it  will  give  the  term  required. 

Note.  When  the  exponent  one  stands  over  the  second 
term,  the  number  of  exponents  must  be  one  less  than  the 
number  of  terms. 

EXAMPLES. 

1.  A  man  agrees  for  12  peaches,  to  pay  only  the  price  of 
the  last,  reckoning  a  farthing  for  the  first,  a  halfpenny  for 
the  second,  ^c.  doubling  the  price  to  the  last  ;  what  must 
he  give  for  them  ? 

0,  1,  2,  3,    4  exponents.  16=4 

1,  2,  4,  8,  IG  number  of  terms.  16=4 


b=3 

4-f4+3=:ll,  number  of  terms  less  1,— r 

4)2018=11  num.  farth. 

12)i:12 

20)42   8 

Ans.  £2  2  8 
2.  A  country  gentleman,  going  to  a  fair  to  l>ny  some  oxen, 
nif^ets  wnh  a  person  who  had  2.^  ;    lie  demand sno-  the    [)rxe 
•f  them  was  answei:ed  JjliS  apiece  ;  Uie  jjenileman  bido  him 


PROGRESSION.  221 

£15  apiece,  and  he  would  buy  all;  the  other  tells  him  it 
would  not  be  taken,  but  if  he  wonld  give  what  the  last  ox 
would  come  to,  at  a  farthing  for  the  tirst,  and  doubling  it  to 
the  la9t,  he  should  have  all.    What  was  the  price  of  the  oxen  ? 

Ans.  £4369  U,  4rf. 


In  aay  Geometrical  Progression,  not  proceeding  from 
unity,  the  ratio  being  given,  to  lind  any  remote  term,  with- 
out producing  all  the  intermediate  terms. 

Rule,  Proceed  as  in  the  last,  only  observe  that  every 
product  must  be  divided  by  the  first  term. 

EXAMPLES. 

1 .  A  «um  of  money  is  to  be  divided  among  eight  persons^ 
the  tirst  to  have  £^20,  the  second  £60,  and  so  on  in  triple 
porportion  :  what  will  the  last  have  ? 

640x510  14580X60 

0.       1.       2.       3. =14500    then =4374« 

20.     60.  180.  540.       20  20 

Ans.  £443740. 
3+3-f  1=7  one  less  than  the  number  of  terms. 

?.  A  gentleman,  dying,  left  9  sons,  to  whom  and  to  his 
«xecutor  he  bequeathed  his  estate  in  the  manner  following: 
To  his  executor  £50  ;  his  youngest  son  was  to  h^ive  as  much 
more  as  the  executor,  and  each  son  to  exceed  the  next 
younger  by  as  much  more  ;  what  was  the  eldest  son's  per* 
lion  ?  Ans.  £25G00. 


The  first  tenn^  ratio  andmunher  of  terms  given ^  to  find  the  sum 
of  (ill  the  terms. 

Rule.  Find  the  last  lorm  as  bofore,  then  subtract  the 
fir^t  from  it,  and  divide  the  remainder  by  the  ratio  le?-s  oce, 
to  the  quotient  of  which  add  the  greater,  and  it  gives  the 
sum  required. 

EXAMPLES. 

1.   A  servant  skilled  in  nur!ibcrs  agreed  with  a  gentlcmaa 
to  serve  him  12  mouilis  provided  he  would  give  him  a  farth- 
U  2 


222  PERMUTATION, 

in^  for  his  first  month^*  service,  a  {  e-.inv  for  the  second,  and 
4iL  for  the  third,  mc.  :  what  did  his  wages  amoim'  to? 

256x26G=G55:i6,  then  6i).;3    Xb4-- 4,9  1304 

0.  1.     2.     3.  4.  4I943U4— 1 

1.  4.    16.   64.     256. =1398101,  then 

(4-f  4  +  3=11.  No.  of  terms  less  1.)  4—1. 

1398101+4194304=5592405  farthings. 

Ans.  £5825  8*.  5|J. 

2.  A  man  bought  a  horse,  and  by  agreement  was  to  give 
a  farthiiig  for  the  first  nail,  three  for  the  second,  &,c. ;  there 
were  4  shoes,  and  in  each  shoe  0  nails  :  what  was  the  worth 
of  the  horse?  Ans.  £965114681693   13*.  4d. 

3.  A  certain  person  married  his  daughter  on  new  year's 
day,  and  gave  her  hushand  one  shilling  towards  her  portion, 
promising  to  double  it  on  the  tirst  day  of  every  month  for 
one  year:  what  was  her  portion  ?  Ans.  £^^04    155. 

4.  A  laceman,  well  versed  in  numbers,  agreed  with  a  gen- 
tleman to  sell  him  22  yards  of  rich  gold  brocaded  kce  for 
2  pins  the  first  yards,  6  pins  the  second,  &ic.  in  triple  pro- 
portion. 1  desire  to  know  what  he  sold  the  lace  for,  if  the  pins 
were  valued  at  100  for  a  iarthing:  also,  what  the  laceman 
got  or  lost  by  sale  thereof,  supposing  the  lace  stood  him  in  £7 
per  yard.  Ans.  The  lace  sold  for  £326886  06-.  2d. 

Gain  £326732  0*.  9c/., 


PERMUTATION 

h  the  changing  or  varying  of  the  order  of  thinji:s. 

Rule  Multiply  all  the  given  terms  one  into  another,  and 
the  last  product  will  be  the  number  of  changes  required. 

EXA.MI'LF.S. 

1.  How  many  chancres  m  »y  be  rung  upon  12  belh,  and 
how  long  would  they  he  rini^uig  but  once  over,  supposing 
10  changes  might  he  rung  m  one  minute,  and  the  year  to 
contain  365  days  6  hours  ? 

1X2X3X4X5X6X7X8X9X10X11X12=479001600 
changes,  -7-  10=47900160  m  nutes,  and  if  reduced  is  =  91 
jears,  3  weeks,  5  days  and  6  hours. 


5Q[T\HE  ROOT.  22S 

t.  \  young-  scholar,  coming  into  a  town  for  the  conYenien- 
cv  of  a  t^ooil  library,  dem  in<ls  of  a  gentleman  wj(ii  whom  he 
lod::>*e<l  what  his  diet  would  cost  for  a  year,  who  told  him 
ij\0  ;  but  the  scholar,  not  beini(  certain  what  time  ho.  sbouUl 
stav,  asked  him  what  he  should  give  him  for  so  ioug  a<^  he 
c<)uld  place  his  family  (consisting  of  6  persons  beside  him- 
s<^lf)  hi  di'Jerent  positions  every  day  at  dinn^M-;  th  •  gentle- 
mm  thhiking  it  could  not  be  long,  tells  him  1^5,  to  whtch 
the  'jcholar  agrees  :  what  time  did  the  scholar  stay  with  the 
gentleman  ?  Ans.  5040  days 


EXTRACTION  OF  THE  SQUARE  ROOT. 

Extracting  the  Square  Root  is  to  find  out  such  a  number 
a>5  being  multiplied  into  itself  the  product  will  be  equal  to 
th;-  given  numbor. 

KuLti:.  1.  Point  the  given  numher,  beginning  at  the  nnit-3 
place,  then  lo  the  hundred's,  and  so  upon  every  second  fig- 
ure througliout. 

2.  Seek  the  greatest  square  number  in  the  first  point,  to- 
wards the  left  hand,  placing  the  squire  number  under  tbe 
first  point,  and  the  root  thereof  m  the  quotient:  subtract  the 
square  number  from  the  first  point,  and  to  the  remamder 
braig  down  the  next  po*nt,  and  call  that  the  resolvend. 

3.  Double  the  quotient,  and  place  it  for  a  divisor  on  the 
l"!!  hand  of  the  resolvend  ;  seek  bow  ot'ten  the  divisor  is  con- 
tained in  the  resolvend,  (reserving  always  the  unit's  place) 
and  put  the  answer  in  the  quotient,  and  also  on  the  right 
hand  side  of  the  divisor;  then  multiply  by  the  figure  last 
put  in  the  quotient,  and  subtract  the  product  from  the  res(d- 
vend;  1)ring  down  the  next  point  to  the  remainder,  (if  there 
be  any  more)  and  proceed  as  before. 

Roots.  I.     2.     3.     4.     5.     (3.     7.     8.     9. 

Squares.      1.     4.     9.   Itj.  25.  3U.  49.  64.  81. 


Mi  iJQUARE  ROOT. 

EXAIMFLKS. 

1.  What  is  the  square  root  of  119025  ? 

119025)345 
9 

64)290 
256 

685)3425 

3425  Ans.  345 

2.  What  is  the  square  roet  of  106929  ?      Ans.  327 

3.  What  is  the  square  root  of  2268741  ?    Ans.    Ia06,23-f- 

4.  What  is  the  square  root  of  7596796  ?  Ans.    2756,228+ 

5.  What  is  the  square  root  of  36372961  ?   Ans.  6031 

6.  What  is  the  square  root  of  22071204  ?  Ans.  4(i98 
When  the  given  number  consists  of  a  whole  number  and 

elecimals  together,  make  the  number  of  decimals  even,  bj 
adding  ciphers  to  them,  so  that  there  mdj  be  a  point  fall  oa 
the  unit's  place  of  the  whole  numbe:. 

7.  What  is  the  square  root  of  327 1 ,4007  ?     Ans.  57, 1 9+ 

8.  What  is  the  square  root  of  4795,25731  ?  Ans.  69,2474- 

9.  What  is  the  square  root  of  4,372594?     Ans.  2,091-f. 

10.  What  is  the  square  root  of  2,2710957?  Ans.  1,50701  + 

1 1.  What  is  the  square  root  of  ,00032754  ?    Ans.  ,01809+ 

12.  What  is  the  square  root  of  1,270054  ?  Ans.   1,1269+ 


To  extract  the  Square  Root  of  a  Vulgar  Fraction, 
RuLK.     Reduce  the  fraction  to  its  lowest  terms,  then  ex- 
tract the  square  root  of  the  numerator  for  a  new  numerator, 
and  the  square  root  of  the  denominator  for  a  new  denomi- 
nator. 

If  the  fraction  hn  a  surd,  (i.  e.  a  number  whose  root  can 
never  be  exactly  found)  reduce  it  to  a  decimal,  and  extract 
the  root  from  it« 

KXAMPLES. 


13.  What  is  the  square  root  of  |  J||  ?         Ans.  | 

14.  What  is  the  square  root  of  f^Jj  ?         Ans.  |. 

15.  What  is  ihe  square  root  of /-^-.'^s.  ?         ^jjg^  . 


SQUARE  ROOT. 


Ce. 


f5 


^V^J^  e>  ^ 


Surd's. 

16.  What  is  the  square  root  of  fff-?  .  Ans.  ,89802+ 

17.  What  is  the  square  root  of  If  ^?  Ans.  ,866t>24- 

18.  What  is  the  square  root  of  fj|  ?  ^ns.  ,93308-f 


To  extract  the  square  root  of  a  mixed  number. 

Rule.  1.  Reduce  the  fractional  part  of  the  mixed  number 
to  its  lowest  term,  and  then  the  mixed  number  to  an  impro- 
per fraction. 

2.  Extract  the  roots  of  the  numerator  and  denominator 
for  a  new  numerator  and  denominator. 

If  the  mixed  number  given  be  a  ^^urd,  reduce  the  frac- 
tional part  to  a  decimal,  annex  it  to  the  whole  number,  and 
extract  the  square  root  therefrom. 

EXAMPLES. 

19.  What  is  the  square  root  of  51  If  ?  Ans.  7^ 

20.  What  is  the  square  root  of  27,^^  ?  Ans.  5^^ 

21.  What  is  the  square  root  of  9||  ?  Ans.  ^ 

Surds. 

22.  What  is  the  square  root  of  85f-|?  Ans.  9,27  + 

23.  What  is  the  square  root  of  8f  ?  Ans.  2,9519  + 

24.  What  is  the  square  root  of  6|  ?  Ans.  2,5298  + 

Thp:  Application. 

1.  There  is  an  army  consisting  ot  a  certain  nnm!)er  of 
men,  who  are  placed  rank  and  hie,  that  is,  in  the  form  of  a 
square,  each  Side  hnviUg  576  men  ;  i  desire  to  know  how 
many  the  whole  square  contains?  Ans.  351770 

2.  A  certain  |)avement  is  made  exactly  square,  each  side 
of  which  contains  97  feet;  I  demand  how  many  squan^  feet 
are  contained  therein  ?  Ans.  9409 


To  find  a  mean  proportirmol  huxi^een  any  Uen  q'lven  numbers. 

KuLK.     The  «qu;«re  ront  of  the  product  of  the  given  num- 
ber is  the  mean  proportional  sou;;;ht. 


22G  SQUARE  ROOT. 


1.  Whr^t  is  the  mean  proportional  lietween  3  and  12  ? 
Ans.  :>X  1^=36  then  ^:^{)=zid  the  mean  proportional. 

2.  What  is  the  mean  proportional  between  4276  and  848  5 

Ans.   1 897,4 -f 


To  find  the  side  of  a  square^  equal  in  area  to  any  given  tuperficiet. 

Rule.     The  square  root  of  the  content  of   anj  giren  u%- 
periicies  is  the  square  equal  sought. 

EXAMPLES. 

3.  If  the  content  of  a  given  circle  be  160,  what  is  the  side 
•f  the  square  equal  ?  Ans.    12,6491 1 

4.  if  the  area   of  a  circle  is  750,   what  is  the  side  of  the 
square  equal?  An*.  27,38612 


The  area  of  a  circle  given^  to  find  the  diameter. 

Rule.  As  355  :  452,  or  as  1  :  1,273239  :  :  the  area  i% 
the  square  of  the  diameter  ;  or,  multiply  the  square  root  of 
the  area  by  1,12837,  and  the  product  will  be  the  diameter. 


5.  What  length  of  cord  will  fit  to  tie  to  a  cow's  tail,  the 
other  end  fixed  in  the  ground,  to  let  her  have  liberty  of  eat- 
ing an  acre  of  grass,  and  no  more,  supposing  the  cow  and 
tail  to  be  5  yards  and  a  half?  Ans.  G,136  perches. 


The  area  of  a  circle  given^  to  find  the  periphery^  or  circiimfc  rente. 

RuLK.  As  1 13  :  1420,  or  as  I  :  12,56637  ::  the  area : 
quare  of  tlie  periphery;  or  multiply  the  square  root  of  the 
irea  by  3,5  149,  and  the  product  is  the  circumference. 


area 


SQUARE  ROOT. 


221 


EXAMPLES. 


6.  When  the  area  is  12,  what  is  the  circumference  ? 

Ans.    12,2798 

7.  When  the  area  is  160,  what  is  the  peripliery  ? 

Ans.  44,84 


Any  two  sides  of  a  right  angled  triangle  givcn^  to  find  the  third 

side. 

1.  The  base  and  perpendicular  given,  to  find  the  hypo- 
thenuse. 

Rule.  The  square  root  of  the  «!um  of  the  squares  of  the 
l»ase  and  perpendicular  is  the  length  of  the  hypothenuse. 


S.  The  top  of  a  castle  from  the  ground  is  45  yards  high, 
and  is  surrounded  with  a  ditch  60  yards  broad  ;  what  length 
must  a  ladder  be  to  reach  from  the  outside  of  the  ditch  t© 
the  top  of  the  castle  ?  Ans.  75  yardf. 


Ditch. 


Base,  60  yards. 

9.  The  wall  of  a  town  is  25  feet  high,  which  is  surround- 
ed by  a  moat  of  30  feet  in  breadth  ;  I  desire  to  know  the 
length  of  a  ladder  that  will  reach  from  the  outside  of  the 
moat  to  the  top  of  the  wall.  Ans.  39,05  feet. 

■^; 


Thchypothenuse  and  perpendicular  given^  to  find  (he  base. 

Rule.  The  square  root  of  the  difference  of  the  squares 
of  the  hypothenuse  and  perpendicular  is  the  length  of  the 
base. 


223  CUBE  ROOT. 

The  hafit  and  hypothenuse  given^  to  find  the  perpendicular. 

Rule.    The  square  root  of  the  difference  of  the  hypothe 
nuse  and  base  is  the  height  of  the  perpexuiicular. 

N.  B.  The  two  last  questions  miiy  be  varied  for  examples 
to  the  two  last  propositions. 


Any  number  of  men  being  given^   to  form  them  into  a    square 
battle^  or  to  find  the  number  of  ranks  and  files. 
Rule.    The  square  root  of  the  number  of  men  given,  is 
the  number  of  men,  either  in  rank  or  file. 

10.  An  army  consisting  of  331776  men,  I  desire  to  know- 
how  many  in  rank  and  liie.  Ans.  576 

11.  A  certain  square  pavement  contains  48841  square 
stones,  all  of  the  sfime  size  ;  1  demand  how  many  are  con- 
tained in  one  of  the  sides?  Ans.  221 


EXTRACTION  OF  THE  CUBE  ROOT. 

To  extract  the  Cube  l^oot  is  to  find  out  a  number  which, 
be^n?:  multiplied  into  itself,  and  then  into  that  product,  pro- 
duceth  the  given  number. 

lluLK.  1.  Point  a^jevy  third  figure  of  the  cube  given,  be- 
2:inning  at  the  unit's  place  :  seek  the  greatest  cube  to  the 
first  point,  and  subtract  it  therefrom  ;  put  iho  root  in  the 
quotient,  and  bring  down  the  figures  in  the  next  point  to  the 
remrtinder  for  a  resolvend. 

2.  Find  a  divi^^or  by  multiplying  the  square  of  the  quo- 
tient by  3.  See  how  often  it  is  contained  in  the  resolvend, 
rejectiHg  the  units  and  tens,  and  put  the  answer  in  the  quo- 
tient. 

3.  To  find  the  subtrahend.  1.  Cube  the  last  figure  in  the 
quotient.  2.  Multiply  all  the  figures  in  the  quotient  by  3, 
exeept  the  last,  and  that  product  by  the  square  of  the  last. 
3.  Multiply  the  divisor  by  the  last  figure.  Add  these  pro- 
ducts together  gives  the  subtrahend,  which  subtract  from 
the  refiolvend  ;  to  the  remainder  bring  down  the  next  point, 
and  proceed  as  before. 

Roots.       I.  2.         3.  4.        5.        6.        7.        8.        9 

Cubes.      1.         8.       27.       64.    125.    216.    313.    512.    729 


CUBE  ROOT.  ^^^^ 


"What  is  the  eube  root  of  99252847  ? 

99252847)403 
64i=cufee  of  4 

Divisor.  

Square  of  4X<3=48)35252  Resolvend. 

216=:Cube  ofG. 
432  ==4x3Xby  square  of  G. 
288     =Divisor  x  by  b. 

33336  Subtrahend. 

Divisor. 

Sq.    of  46X3=6348)1916847   Resolvend. 

27=:Cube  of  3. 
1242  =46  x3xby  square  of  3. 
19044     =DiYisor  X  by  3. 

1916847   Subtrahend. 


Jinolher  nea>  and  more  concise  method  of  extracting  the  Cube 

Root. 

Rule.     I.  Point  every  third  llgure  of  the  cube  given,  be- 
ginning* at  the  unit's  place,  then  tind  the  nearest  cube  to  the 
rst  point,  and  subtract  it  therefrom,  put  the  root  in  the  quo- 
tient,   brins:  down  the  %ures  in  the    next  point    to  the  re- 
mainder for  a  resolvend. 

2.  Square  the  quotient  and  triple  the  sq\iare  for  a  divisor: 
-,  4X4X3=18.     Find  how  often  it  is  contained  in  the  re- 

rioivend,  rejectiiig  units  and  tens,  and  put  the  answer  in  the 
quotient. 

3.  Square  the  last  fi«fure  in  the  quotient,  and  put  it  on  the 
right  hand  of  the  divisor. 

As  6X6=36  put  to  the  divisor  48=4836. 

4.  Triple  the  last  figure  in  the  quotient,  and  multiply  by 
the  former,  put  it  under  the  other,  units  under  the  tens,  add 
them  together,  and  multiply  the  sum  by  the  last  figure  in  the 
quotient,  su'^ti-arl  that  product  from'  the  Resolvend,  bring 
down  the  next  point,  and  proceed  as  before. 

X 


230  CUBE  ROOT. 

EXAMPLCS. 

1.  What  is  the  cube  root  of  99252847  ? 

Square  of  4X3=48  divisor.  99252847(463 

Sfjuare  of  6  put  to  48=4i]i56  64 

6X3X4=  72  

35252 

5556        X        6  =    33oo6 

Sqnare     of  46—21 16x^=6348  divisor 

Square  or3--=r9  put  to  634P.==:*b348u9  193  6847 
3X3X46=       414 


6o89i9x3=1916847 

2.  What  is  the  cube  r-^ot  of  38:^01 7?  Aus.   73 

3.  What  is  the  cube  root  ot  5"/ 35339?  Ans.    J  79 

4.  What  is  the  cul.e  root  of  32461759  ?  Ans.  319 

5.  What  is  the  cube  root  of  84604519?  Ans.  439 

6.  What  is  the  cube  root  of  2  >9694U72  ?  Ans.  638 

7.  What  is  the  cube  root  ol  48228544?  Ans.  364 

8.  What  is  the  cube  root  of  27(i54('36()08  ?  Ans.  3U02 

9.  What  is  the  cube  root  of  22069^810125  ?  Ans.  28U5 

10.  What  is  the  cube  root  of  12^61532^232?       Ans.  4i^68 

11.  What  is  the  cube  root  of  2I9S65,5277!U  ?       Ans.  6031 

12.  What  is  the  cube  root  of  673373097  125  ?       Ans.  8765 

When  the  given  number  consists  of  a  whole  number  and 
decimal  together,  make  the  number  of  decimals  to  con5;ist  of  - 
3,  6,  9,  &:c   places,  by  adding  ciphers  thereto,  so  that  there 
may  be  a  point  fall  on  the  unit's  place  of  the  whole  number. 

13.  What  is  the  cubo  root  of  12,977875?         Ans.  2,35 

14.  W^hat  ir«  the  cube  root  of  361  55,027576  ?  Ars.  33.06  + 

15.  W^hat  is  the  cul)e  root  of  ,001906624  ?       Ans.  ,124 

16.  What  i«  the  cube  root  ©f  33,230979637?   Ans.  3,215  + 

17.  What  is  the  cube  root  of  15926,972:04?    Ans.  25,16+ 

18.  What  is  the  cube  root  of  ,053258279  ?         Ans.   ,376  + 

*  When  il)0  quotient  is  1,  2  or  S,  there  must  be  a  cipher  put  to  supply 
the  place  6f  tens. 


CUBE  ROOT.  231 

To  extract  the  Cube  Root  of  a  Vulgar  Fraction. 

Rule.  Re.iuce  the  fniction  to  its  lowest  terms,  then  ex- 
tract the  cube  root  ©f  the  numerator  and  denominator  ibr  a 
new  numerator  and  denominator;  but  if  the  fraction  be  a 
surd,  reduce  it  to  a  decimal,  and  then  extract  the  root  from  it. 

s  EXAMPLES. 

19    AVhat  is  the  cube  root  of  f  f|t  ?  Ans.  f 

2%.  What  is  the  cub3  root  of  //-^,y  ?  Ans.  | 

21.  What  is  the  cube  root  of  If* a?  Ans.  1 

SURDS. 

22.  What  is  the  cube  root  of  4  ?  Ans.  ,8204- 

23.  What  is  the  cube  root  of  a  ?  Ans.  ,82^J-f 

24.  What  is  the  cube  root  of  J?  Ans.  ,873+ 


To  extract  the  Cube  Root  of  a  Mixed  Kumbcr. 

Rule.  Reduce  the  fractional  part  to  its  lowest  terms,  and 
then  the  mixed  number  to  an  improper  fraction  ;  extract  the 
cube  roots  of  the  numerator  and  denominator  for  a  new  nu- 
merator and  denominator :  but  if  the  mixed  number  given 
be  a  surd,  reduce  the  fractional  part  to  a  decimnl,  annex  it 
to  the  whole  nuoiber,  and  extract  the  root  therefrom. 

EXAMI'LKS. 

25.  What  rs  the  cube  root  of  12.]}  ?  Ans.  2} 

26.  What  is  the  cube  root  of  3IJ^%?  Ans.  3| 

27.  What  is  the  cube  root  of  405//^?  Ans.  7f 

Sunns. 

28.  What  is  the  cube  root  of  7}  ?  Ans.   1,93  + 

29.  What  is  the  cube  root  of  9J^^  ?  Ans.  2,092+ 

30.  What  is  the  cube  root  of  84?  Ans.  2,057  + 


252  CUBE  ROOT. 

The  ArpLicATiOx\. 

1.  If  a  cubical  piece  of  timber  be  47  inches  long,  47  inches 
broad,  and  47  inches  deep,  how  many  cubical  inches  doth  it 
contain?  Ans.   103823 

2.  There  is  a  cellar  dug  that  is  12  feet  every  way,  in 
length,  breadth  and  depth ;  how  many  solid  feet  of  earth 
were  taken  out  of  it?  Ans.    1728 

3.  There  is  a  stone  of  a  -cubic  form,  which  contains 
389017  solid  feet:  what  is  the  superficial  content  of  one  of 
its  sides  ?  Ans.  6329 


Betzveen  two  numbers  givcn^  to  find  two  mean  proportionals. 

Rule.  Divide  the  greater  extreme  hy  the  lesser,  and  the 
cube  root  of  the  quotient  multiplied  by  the  lesser  extreme 
gives  the  lesser  mean :  multiply  the  said  cube  root  by  the 
lesser  mean,  and  the  product  will  be  the  greater  mean  pro- 
porticnaL 

EXAMPLES. 

4.  What  are  the  two  mean  proportionals  between  6  and 
jG2?  Ans.   18  and  54. 

5.  What  are  the  two  mean  proportionals  between  4  an4 
108?  Ans.   12  and  36. 


To  find  the  side  of  a  cube  that  shall  he  equal  in  solidity  to  any 
given  solid^  as  a  globe^  cylinder^  prism^  cone^  4'C. 

Rule.     The  cube  root  of  the  solid  content  of  any  solid 
body- given,  is  the  side  of  the  cube  of  equal  solidity. 

EXAMPLE. 

6.  If  the  solid  content  of  a  globe  is  10648,    what  is  the 
r^ide  of  a  cale  of  equal  solidity?  Ans.  2^ 


BIQUADRATE  ROOT.  233 

T^ie  side  of  a  cube  being  given^  to  find  the  side  of  that  cube 
that  shall  be  double^  treble^  <S*c.  in  quantity  to  the  given  &ube. 
RuLK,     Cube  the  side  given,  and  multiply  it  by  2,  3,  &c. 
the  cube  root  of  the  product  is  the  side  sought^ 

EXAMPLE. 

7.  There  is  a  cubical  vessel  whose  side  is  12  inches,  and 
it  is  required  to  fuid  the  side  ot\another  vessel  that  is  to  con- 
tain three  times  as  much  ?  Ans.  17,306 


EXTRACTION  OF  THE  BIQUADRATE 
ROOT. 

To  extract  the  Biquadrate  Root  is  to  find  out  a  number, 
which,  being  involved  lour  tim*es  into  itself,  will  produce 
the  given  number. 

Rule.  First  extract  the  square  root  of  the  given  number, 
then  extract  the  square  root  of  that  square  root,  and  it  will 
give  the  biquadrate  root  required. 

EXAMPLES. 

1.  What  is  the  biquadrate  of  27?  Ans.  531441 

2.  What  is  the  biquadrate  of  76?  33362176 

3.  What  is  the  biquadrate  of  275?  5719140G25 

4.  What  is  the  biquadrate  root  of  531441  ?  27 

5.  What  is  the  biquadr  ite  root  of  338G2I76?  7G 

6.  What  is  the  biquadrate  root  of  5719140625?  275 


A  GENERAL  RULE 

FOR    EXTRACTIING    THE    ROOTS    OF    ALL    POWERS. 

1.  Prepare  the  number  given  for  extraction,  by  pointings 
eH'from  the  unit's  place,  as  the  root  required  directs. 

2.  Find  the  first  figure  in  the  root,  by  the  table  of  powers, 
which  subtract  irom  the  given  number! 

X2 


231  RULE  FOR  EXTRACTING,  kc, 

3.  Brio^'  down  the  (irst  lig-ure  in  the  next  point  to  the 
remainder,  and  call  it  the  dividend 

4.  Involve  the  root  into  the  next  inferior  povver  to  that 
which  is  given  j  multiply  it  by  the  given  power,  and  call  it 
the  divisor. 

5.  Find  a  quotient  figure  bj  common  division,  and  annex 
it  to  the  root;  t'len  involve  the  whole  root  into  the  given 
power,  and  call  that  the  subtrahend. 

6.  Subtract  that  number  from  as  many  points  of  the  given 
povver  as  is  brought  down,  beginning  at  the  lowest  place, 
and  to  the  remainder  bring  down  the  first  figure  of  the  next 
point  for  a  new  dividend. 

7.  Find  a  new  divisor,  and  proceed  in  all  respects  as  be- 
fore. 

EXAMPLKS. 

1.  What  is  the  square  root  of  141376? 

141316(376 
9 

6)51   dividend.  3X2=6      •    divisor. 

37X37  =  1369  subtrahend 

1369  subtrahend.    .      ^     37X2=^74         divisor. 

376X376=141376  subtrahend. 


74)447  dividend. 


141376  sul4rahend.  Ans.  676 

2.  What  is  the  cube  root  of  53157376  ? 

53157376(376 
27 


27)261   dividend.  3X3X3=37  divisor. 

37X37X:'^7^5065  subtrahend. 

50653  subtrahend    :37X37X?^^  H'^'?  divisor. 

376X376X37e— 53157376  subtrahend. 

4107)25043  dividend. 

53157376  subtrahend.  Ans.  376 


DUODECIMALS.  23* 

3.  What  is  the  biquadrate  root  of  19987173376  ? 

19087173376(376 
81 


108)1188  dividend. 


1874161   subtrahend. 


202612)      1245563  dividend. 

19087173376  subtrahend. 

3X      3X      3X      4  =108  di\Msor. 
37    X    37    X    37   X   37  =    1874161   subtrahend 
37    X    37    X      3    X      4  =   202o  i  2  dr/isor. 
376   X376   X  376       376  =-z   19087173375  subtrahend. 

Ans.  37G. 


DUODECIMALS. 

DiTODEciMALS,  or  Cross  Multiplication,  is  a  rule  made  use 
©f  in  measuring  and  comi>uting  the  dimensions  of  the  ?-eviM"al 
parts  of  buildiiii^s  ;  it  is  likewise  used  to  iind  ships'  tonnage, 
and  the  contents  of  bales,  cases,  4rc. 

Dimensions  are  taken  in  feet,  inches  and  parts. 

Artifieers'  work  is  computed  by  diiTt^-ent  measures,  viz. 

Glazing,  and  masons'  flat  work,  by  the  foot. 

Painting,  pavins^,  plastering",  &c.  by  the  yard. 

Partitioning,  flooring,  roofing,  tiling,  &c.  by  (lie  square  of 
100  feet. 

Brick-work,  kc.  by  the  rod  of  IG^  ft.  who^e  square  is  2T2'- 

The  contents  of  bales,  cases,  &c.  by  the  ton  of  40  cubic 
feet. 

The  tonnage  of  ships,  by  the  ton  of  95  feet. 


23k:^  duodecimals. 

lilTLE  FOR  MULTIPLYLXa  DUODECIMALLY, 

1.  Under  the  multiplicand  write  the  corresponding  de- 
nominations of  the  multiplier. 

2.  Multiply  each  term  in  the  multiplicand  (beginninsf  at 
the  lowest)  by  the  feet  in  the  multiplier;  write  each  result 
under  each  rej^pective  term,  observing  to  carry  an  unit  from 
each  lower  denomination  to  its  superior. 

?j.  In  the  same  manner,  multij)ly  the  multiplicand  by  the 
inches  in  the  multiplier,  and  write  the  result  of  each  term 
one  place  more  to  the  right  hand  of  them  in  the  multipli- 
cand. 

4.  Work  in  the  same  manner  with  the  other  parts  in  the 
multiplier,  setting  the  result  of  each  term  two  places  to  the 
right  hand  of  those  in  the  multiplicand,  and  so  on  for  thirds, 
fourths,  <S'C. 

5.  Proceed  in  the  like  manner  w^lth  all  the  rest  of  the 
denominations,  and  their  sum  will  give  the  answer  required. 

EXAMPLES. 

I.  Multiply  4  feet  9  inches  by  8  inches. 

ft.   in. 
4     9 


3     2  Ans.  S  fe^ei  2  inches 

2.     Multiply  9  ^eei  6  inches  by  4  feet  9  inches. 
ft.  in. 
9     6 
4     9 

ft.  in.  

*  9     'XI   feetc=38     0 
9     tX9  in.  =  7     1     6 


45      I      6 
Arts.  45  feet  1  inch  and  G  twelfth.* 


DUODECIMALS.  2Si7 

3.  What  is  the  price  of  a  marbie  slab,  whose  length  is  5 
/eet  7  iuches,  and  breadth  1  foot  10  inches,  at  I  dollar  [)er 
foot^  Ads.   10  dolls,  '^b  cents  6  mills. 

4.  There  is  a  house  with  three  tiers  of  windows,  3  in  a 
tier;  ihe  height  of  the  first  tier  is  7  feet  10  inches,  of  the 
second  6  feet  8  inches,  and  of  the  third  5  feet  4  inches,  and 
the  breadth  of  each  is  3  feet  1 1  inchcfs  ;  what  will  the.?-!az- 
ing  come  to  at  \4d.  per  foot?  Ans.  £13   11    10|. 

o.  If  a  house  measure  within  the  walls  52  ieei  8  inr.hes 
in  length,  and  30  feet  G  inches  in  breadth,  and  the  roof  be 
of  a  true  pitch,  or  the  rafters  -j  ot  the  breadth  of  the  build- 
ing, what  will  iU  roofmg  come  to  i\f  lOs.  Sd.  per  square  ? 

Ans.  £12   12   llf 


APPLICATION  OF  DUODECIMALS, 

To  find  how  many  cubic  or  solid  square  feet  {in  order  to  ascer- 
tain the  freight)  are  contained  in  cases^  bales^  ^c.  that  t*,  hoy); 
many  cubic  feet  they  will  take  tip  in  a  ship. 

EXAMPLES. 

1.  Suppose  the  dimensions  of  a  bale  to  be  7  feet  6  inches, 
3  feet  3  inches,  and  1  ibot  10  inches  :  what  is  the  solid  cor- 
tent? 

ft.     in. 
'l       G 
3       3 

ft.    in,  

7     6   X    3  ft.=2S       G 
7     6x3  in.=   1      10     6 


1'4       4     G 
1      10 


ft.    in.  tw. 

24     4     GXl      ft.=24       4     G 

24     4     GxlOin.c=20       3     9 


44       B     3 
Ans.  44  feet  8  inches  and  3  12th  part?. 


238  DUODECIMALS. 

2.  What  is  the  freight  of  a  bale  containing  65  feet  9  inch- 
es, at  15  dollars  pp-r  ton  of  40  feet? 

dolls. cts.  decimally. 

15,00  for  40  feet  ^5,75 

20  fi.     1        7,50  15 

5  ft.     1        1,87,5  

Gill.    yV        ,18,7  32875 

3          1         ,01i,3  6575 


24,65,5  40)986,25 

24,65,6 
Ans.  24  dolls.  65^  cts. 

3.  A  merchant  imports  from  London  6  bales,  of  the  fol- 
lowing dimensions,  viz. 

Length.  Height.  Depth. 

Jt.  in.  ft.  in.  Jt.  in. 

No.  1.  2   10  2     4  19 

2.  2    10  2     6  13 

3.  3     6  2     2  1      S 

4.  2   10  2     8  19 

5.  2   10  2     6  19 

6.  2   U  2     8  1-8 
What  are  the  solid  contents,  and  how  much  will  the  freight 

amount  to,  at  20  dolls,  per  ton  ? 
'The  contents  are,  viz. 

ft.  in.  feet. 

No.  1.              117  71,58 

2.               8   10  29  dolls,  per  ton. 

3  12     7  


4.  13     2  40)1 43 1, HO 

5.  12     5  

6.  13     0  35,79 


71     7  Ans.  35  dolls.  79  cts. 


To  find  5/itpt'  Tontia^e  by  Carpenters'^  Measure. 

Rule.  For  single  decked  vesi^els,  multipij  ihc  length, 
bri^idlh  at  the  main  henm,  r.nd  depth  ©f  the  hold,  tog'ether. 
iind  divide  the  product  by  95. 


DUODECIMALS.  23S 

EXAMPLE. 

Wha^  is  the   tonnasT^  of  a  shio^Ie  dockorl  vespo],  whose 
lei'igih  is  00  leet,  breadth  20  feet,  and  depth  8  ioet? 
CO  leno^th. 
20  breavith. 


1200 

8  depth. 


95)^)600(101/3 
95 


100 
95 


5  An«.   701-5^  ton?. 

This  is  the  usual  method  of  tonna^ing  a  sin^^Ir  decked  vessel  ha^  ing 
the  deck  bolfed  <o  the  walc.  Kui  if  ii  beireoiuied  (hat  the  deck  be 
bol  ed  at  any  height  above  the  wale,  ihe  custom  i^^  10  pay  the  carpenter 
for  oae  half  of  the  addidonal  heiglit  to  which  the  deck  may  be  ihuK  rais- 
ed ;  thai  i-,  o:)e  h.'lf  of  die  difference  beii;g  t'ddtd  o  the  former  depth 
gives  the  dtpih  to  be  us-ed  in  calculaiiiig  the  lOaiiage. 

EXAMILE 

A  merchant,  after  having  coniracted  with  a  cappenter  to 
bu'ld  a  single  (l<  eked  vessel  of  t'O  feet  keel,  20  feet  beam, 
and  8  feet  hold,  desires  that  the  deck  be  laid  lor  10  feet 
hold:  required  the  tonnage  to  be  paid  for. 

60  length. 

20  breadth. 


1200 
l:=^l  diff.  of  depth  -f  8  =      9 

4  

95)10800(11311 
95 

130 
95 


350 

285 


65  Ahs.   113J^  tons. 


Jtu  DUODECIMALS. 

Rule.  For  a  (louble  deckerl  vessel,  take  half  the  breadth 
©f  the  main  beam  for  the  depth  of  the  hold,  and  work  as  for 
a  single  decked  vessjsel. 

EXAMPLES. 

1.  What  is  the  tonnage  of  a  double-decked  vessel,  whes<$ 
length  is  65  feet,  and  breadth  21  feet  6  inches? 
65         length. 
21     6  breadth. 


65 
ISO 
«5  feet  X  6  inches  =      82     6 

1397     6 

10     9  depth. 

1397  ft.  6  in.  X 10  ft.  =   13975     0 
13^7  ft.  6in.x  ^  in-  "^      1048      1 

93)15023     l(15Sii^ 
'     95  '' ' 

552 
^76 

773 

760 


18  Ans.  15811  t©ns 


The  preceding  question  may  be  wrought  thus  : 
65 
21  6 

65 
130 

1365 
Q     k         32  6 

1397  6 
10  9 

13975  0 
6     ^  698  9 

3     ^  349  4 

95)15023   1    as  before 


158'.«   to«is. 


DUODECIMALS.  84 1 

2.  What  will  the  above  tonnage  amount  to,  at  16  dolls, 
per  ton  ? 

dolls. 
158  lt3 

16  13 

948  48 

158  16 


2,18 


95)208(2,18 


253U,ie  190 


180 
95 

850 
760 

90 

Ans.  2530  dolls.  18  cents. 


S.  Required  the  tonnage  of  a  ship  of  74  feet  keel,  and  26 
feet  6  inches  beam.  Ans.  273f  |  tons. 


To  find  the  Government  Tonnage, 

"If  the  vessel  be  double  decke<l,  take  the  length  thereof 
from  the  fore  part  of  the  main  st^m,  to  the  after  part  oi' the 
stern  post,  above  the  upper  deck ;  the  breadth  thereof  at 
the  broadest  part  above  the  mnin  wak  s,  half  of  which  breadth 
gliall  be  accounted  the  depth  of  such  vessel,  and  then  deduct 
from  the  len-^th  three  fifths  of  the  breadth,  muliiply  the 
rpm:under  by  th'^  breadth,  and  the  product  by  the  depth,  and 
divide  thi?*  Ia>t  product  by  95,  the  quotient  whereof  shall  be 
deemed  the  true  contents  or  tonnage  of  such  ship  or  vessel; 
and  if  such  ship  or  vessel  be  single  decked,  take  the  length 
and  breadth,  as  above  directed,  deduct  from  the  said  length 
Y 


.24S  DUODEriMALS. 

three  fifths  of  the  breadth,  and  lake  the  depth  from  the  un- 
der side  of  the  deck  plank,  to  the  ceilins:  m  th«^  hold,  then 
multiply  and  divide  as  aforesaid,  and  the  quotient  shall  be 
fleemed  the  tonnage." 

EXAMPLES. 

1.  What  is  the  government  tonnage  of  a  single  decked 
Tes?el,  whose  length  is  69  feet,  6  inches,  breadth  22  feet  6 
inches,  and  depth  8  feet  6  inches  ? 

ft.  in. 

69  6  lensrth.  22  6  breadth, 

deduct  13  6  for>  breadth.  3 


56  0  5)67  6 

22  6  breadth.  

13  6 


112  0 
112 

6  in.  I         28  0 


1260  0 

8  6  depth. 


10080  0 


9  in.  J         630  0 


95)10710  0(il2J|  tons. 
95 

121 

95 

260 
190 

70 


Ans    11211  tons. 


DUODECIMALS.  248 

2.  What  is  the  government  tonnage  of  a  double  docked 
vessel,  of  the  following  dimensions  ;  length  75  feet  G  inches^ 
breadth  23  feet  4  inches,  and  depth  11  feet  8  inches? 

ft.  in. 
75  6 
14  0  for  I  breadth. 

61   0 

23  4  breadth. 


183  61  ft.  X  23  ft.=:1403  0 

122  6  in.    X  23  ft.=      11   6 

«  in.  I       116  61  ft  6  in.  X  4  in.=     20  6 

4  in.  ^       20  6  


1435  0 

1435  0  118 

1 1   8  depth.  

lo785 

15785  0  1435  ft.  X  8  in.=     956  8 

6  in.  1       717  6  

t  in.  i       239  2  16741  8  as  before. 


95)16741  8(17614  tons. 
95 

724 
665 


591 
570 

21 

Ans.  I76Ji  tons. 

3.  What  is  the  government  tonnage  of  a  double  deck;  3 
Yessel,  of  the  follovvingdimensions;  length  82  feet  3  inches, 
kreadth  24  feet 3  inches,  and  depth   12  feet  U  inches? 

Ans.  '209f  I  tons. 


*'»4  TABLES  OF  CORDAGE. 

TABLES  OF  CORDAGE. 


A  Cordage  Table,  shewing  how  many  fathoms^  feet  and  incheg 
of  a  Rope^  of  any  nze^  not  more  than  1 4  inches^  make  a  hun- 
dred  weight;  with  the  use  of  the  table. 


^ 


eo 

OS 

<;^ 

<aj 

^^ 

-< 

e 

CJ 

sr 

s: 

^-N 

•^ 

o 

'4 

0 

7f 

0 

8 

0 

^ 

0 

»4 

0 

^ 

6 

9 

0 

S'i 

0 

94 

0 

9i> 

0 

'0 

6 

m 

G 

lOi 

n 


4tj6 

313 

216 

159 

124 

96 

77 

65 

54 

45 

39 

34 

30 


0  0 

3  0 

3  0 

3  0 

3  0 

2  0 

3  0 

4  0 

0  0 

5  2 
3  0 
3  9 

1  6 


n 

5 

5i 

O4 
6 
6i, 

6f 
7    ' 
7i 


26   5 

24  0 

21 

19 

17 

16 

14 

13 

12 


n 

10 
9 
9 


103 

n 

Hi 

ill 

12 

\n 

12« 
12J 
13 

131 
13| 
14 


1 

0 
5 
4 
3 
2 
2 
2 
7 
5 
4 
4 
3 
2  2 


Z/6£  OF  THE    TABLE. 

At  the  top  of  the  table,  marked  inches,  fathoms,  ^eei.^  inch- 
es, the  first  cohinnn  is  the  thickness  of  the  rope  in  inches 
and  quarters,  and  the  other  three  the  fathoms,  feet  and  inch- 
es, that  make  up  a  hundred  weight  of  such  a  rope.  One 
example  will  make  it  plain: 

Suppose  you  desire  to  know  how  much  of  a  seven-inch 
rope  will  make  a  hundred  weight ;  find  7  in  the  third  col- 
umn under  inches,  or  thickness  of  rope,  and  aa^ainst  it  in  the 
fourth  column  you  find  9,  5,  6,  which -shews  that  there  will 
he  9  fathoms,  5  feet,  6  inches  required  to  make  up  one  hua- 
dred  weigiit. 


TABLES  OF  CORDAGE, 


246 


A  TxBf.F,  shcxvhifr  the  weight  of  any  Cable  or  Rope  of  1^0 
fatkoins  m  Uiitgtli^  ana  for  every  ha  finch,  from  3  to  iii  1  tncheSy 
in  circunfertucc. 


~3"" 

2  J 

1 

1 

7 

12  I 

'Si 

3  0 

7i 

14  0 

4 

4  0 

8 

16  0 

4i 

5  0 

84 

18  0 

5 

6  1 

9 

20  1 

5i 

7  2 

9i 

22  2 

6   ! 

9  0 

10 

25  0 

6i 

10  2 

m 

27  2 

30  I 
33  0 
36  0 
39  0 
42  1 
45  2 
49  0 


11 

Uh 

12 

13 

I3i 

14  ,  - 

14^  52  2 

15  56  1 


"l5i 

16  I 
I6i| 
17 
17i 

18  i 
18^ 

19  I 
19^1 


00  0 
64  0 
68  0 
72  I 
76  2 
8i  0 
85  2 
90  1 
95  0 


20  , 

20^ 

2;  I 
2li- 

22  j 
22^, 

23  , 
23ii 

24  I 


H 

iOO 

0 

i05 

0 

IIO 

1 

lio 

2 

121 

0 

126 

2 

132 

1 

138 

0 

144 

0 

USE  OF  THE  TABLE. 

The  first  column,  markeil  ior  inches,  is  the  thickness  or 
circumference  of  the  cable  to  every  half  inch  from  6  to  24 
inches;  the  second,  marked  cvvt.  qrs.  for  the  hundred  weights 
and  quarters  that  it  will  weigh  if  120  iathoms  in  length. 

For  instance:  Suppose  it  be  a  cable  of  \A\  mches;  look 
against  14A  and  you  will  find  in  the  other  column  52  cwt.  2 
qrs.  which  shews  that  120  tathoms  of  14^  mch  cable  will 
weigh  52  cwt.  2  qrs.  and  so  in  others  ;  and  any  quantity  of 
a  less  length  will  weigh  in  proportion. 

A  ship  was  hrouglit  to  anchor  in  a  gale  of  wind;  but  the 
gale  increasing,  it  was  thought  safest  to  cut  the  cables,  in 
consequence  of  which  75  fathoms  of  16  inches,  and  50  fa- 
thoms of  12  inches  were  losi ;  what  must  they  be  v  ilued  at 
in  calculating  the  average,  new  cordage  being  then  14  dol- 
lars per  cvvt.  ? 

CALCULATION. 
120  fath.  16  in.  cable=64  ewt.  120  fath.  12  in.  cab  =36  cwt* 


60 
15 


do. 
do. 


75  fath.  weighing 
50    do. 


32 
8 


40 
15 


40 
10 


do. 
do. 


12 
3 


60  fath.  wei-;hing        15 


65  cwt.  at  14  dolls,  per  cwt. 
One  third  deducted  lOr  new 


dlls.  cts. 
770  00 
256  662: 


¥2 


Ans   doUs.  513  33^- 


246  TABLES  OF  GOLD  COIN. 

TABLES  OF  GOLD  COIN. 


A  TARLE 

For  receiving  and  paying  the  Gold  Coins  of  Greot-Bntain  and 
Portngal^  of  their  present  sWndard^  at  100  cts.for  ^7  grains^ 
According  to  an  Act  of  Congress,  passed  Ajfyil  29,  \\}\Q. 


grs.     ch.      1 

dzi)t.       dls.  ctt. 

1  (kvt.      (ILs.cts 

1  dz^'t.  dls.  cts. 

1   -      4 

7  -     6   22 

39  -  34   67 

70  -  iJt    ^2 

o  .     7 

8  -     7    11 

40  -  35  55 

71  -  63    11 

3  .    11 

9  -     8  00 

41    -  36  44 

72  -  iy\   00 

4  -   15 

10  -     9   39 

42  -  37  33 

73  -  64   89  : 

5  -   19 

11    -     9  78 

43  -   ^8   22 

74  -  65  78 

6  -  22 

12  -   10  67 

44  -  39    1 1 

75  -  66  67 

7  .  26 

13  -   11    55 

45  -  40  00 

76  -  67   55 

8  -  30 

14  -   12  44 

46       40  8!^ 

77  -  68   44 

9  -  33 

15  -   13  33 

47  -  41    78 

78  -  69   33 

10  -  37 

16  -   14  22 

48   -  42  67 

79  ^  70  22 

11-41 

17  -   15   1 1  ' 

49  -  43  55 

80-71    11 

12  -  44 

18  -   16  00 

50  -  44   44 

81-72  00  ii 

13-48 

19  -   16  89 

51-45  33 

82  -  72  89    • 

14  -  52 

20  -   17   78 

52  -  46  22 

83  -  73   78 

15-56 

21   -  18  67 

53-47    11 

84  -  74   67 

16-59 

22-19  55 

54  -  48  00 

85  -  75  55 

17-63 

23  -  20  44 

55  -  48   89 

86  -  76  44 

18  -  67 

24  -  21   33 

56  -  49  78 

87  -  77   33 

19-70 

25  -  22  22 

57  -  50  67 

88  -  78  22 

20  -  74 

26-23   11 

58  -  51    55 

89  -  79    1 1 

21   -  78 

27  -  24   00 

59  -  52  44 

90  -  80  00 

22  -  81 

28  -  24   89 

60  -  53  33 

9  1  -  80  89 

23  -  85 

29  -  25  78 

61   -  54   22 

92-  81    78 

24  -  89 

30  -  26  67 

62  -  55    1  1 

93  -  82  67 

31-27   55 

63  -  56  00 

94  -  83  55 

dwt.  dllsMs. 

32  -  28  44 

64  -  56  89 

95  -  84  '44 

I    -        89 

33  -  29  33 

65  -  57  78 

96  -  85  33 

2  -   1   78 

34  -  30  22 

66  -  58   67 

97  -  86   22 

3  -  2  67 

35-31    11 

67  -  59  55 

98-  87    11 

4  -  3  55 

36  -  32  00 

68  -  60  44 

99  -  88  00 

5  -  4  44 

37  -  32  89 

69  -  61   33 

100-  88  89 

«  .  6  33 

38  -  33  78 

TABLES  OF  GOLD  COIN. 
A  TABLE 


24*r 


}or  receiving  and  pacing  the  Gold  Coins  of  France^  of  (heir 
present  .standard^  at  100  cents  for  27  t  grains.  According  to 
an  act  of  Congress^  passed  April  29,  1816. 


grs.      cts. 

dwt. 

(Hi.  CIS. 

dxvt.     dls.  cts. 

1  (iz<:t.    fii^.    cts^ 

I  -      1 

7   - 

6    1  1 

39  -  34  U3 

70-61    07 

2-     7 

8  - 

t>   98 

40  -  31  90 

71    '  61    95 

3  -  n     1 

9  - 

7   R5 

41    -  35   77 

72   -  62  82 

4-15       1 

10  - 

8   73 

42  -   36   65 

73  -  G3  69 

5-   18       1 

11    - 

9   i-.O 

43  -  37   52 

74   -  64    57 

6  -  22 

12  - 

10   47 

44  -  38   39 

"5  -  65   44 

7  -  "zo 

13  - 

I  1    34 

45  -  39  26 

76  -  66  31 

8  -  29 

14  - 

12   21 

46  -  40    13 

77  -  67    18 

9-33 

15  - 

13  09 

47  -  41    01 

78  -  68  05 

10  -  36 

16  - 

13  96 

48-41    88 

79  -  68  93 

11  -  ^k) 

17  - 

14  83 

49  -  42   75 

80  -  691180 

12  -   44 

18   - 

15  71 

50  -  43  63 

81    -  70  67 

13-  47 

19  - 

16   58 

51    -  44   50 

82  -  7i    5a 

1  i  -   51 

20  - 

17   45 

52  -   4£»  37 

83  -  72   42 

1  5  -  55 

21    - 

18   32 

53  -  46   24 

84  -  73  29 

16-53 

22   - 

19    19 

51  -  47    1 1 

85  -  74    16 

17  -  62 

2.5  - 

20  07 

55  -  47   99 

86  -  75  03 

13-  65 

24  - 

20  94 

5')  -  4  8   86 

87  -  75  91 

19-89 

25  - 

21    81 

57  -  49   73 

88  -  76   78 

.  50  -  73 

26  - 

22  69 

58  -  50  61 

89  -  77   6o 

21-76 

27  - 

23  56 

59  .  51    48 

90  -  78   53 

22  .  80 

28  - 

24  43 

60  -  52  35 

91-79  40 

23  -  83 

29  - 

25  30 

61    -  53  22 

92  -  80  27 

24  .  87 

30  - 

26    17 

62  -  54  09 

93-81    14 

31    - 

27  05 

il^  .  54  97 
64  -   55   84 

91  -  82  01 
95  -  82  89 

dwl   dla.  cts. 

32  - 

27   92 

1   -       87 

33  - 

28  79 

65  -  56  71 

96  -  83  78 

2  -   1    75 

34  - 

29  67 

GQ  -  57  59 

97  -  84  63 

3  -  2  62 

35  - 

30  54 

67  -  58   46 

08  -  85  51 

4  -  3  49 

36  - 

31    41 

68  .  59  33 

Vk)  -   86   38 

5  -  4  36 

37  - 

32  28 

69  -  60  20 

'  100  -  87   25 

6  -  5  23 

38  - 

33   15 

i48 


TABLES  OF  GOLD  COLTST. 


A    TABLE 


For  receiving  and  paijini{  Om  Gold  Coins  of  Spahi^  and  ike 
doininlous  of  Spain^  (f  thc>r  prcatnt  dnwJard^  at  iOO  cents 
for   2^'>\    irrams.     Accordmg  to  an  act  of  Congress^  jjamed 


•.  r.v 

cts. 

1  ■r.t. 

aL. 

I  -  ic'(.  dis. 

et.s. 

1  d-ci^t.     ://■.';.  rts. 

J 

-   3 

7  - 

5 

oo 

3H  -  32 

7  6 

70  -  58  80 

2 

-  7 

8  - 

6 

7^ 

40  -  33 

6m 

71  -  59  64 

S 

-  )  1 

9  - 

7 

56 

41  -  34 

44 

72  -  60  48 

4 

-  14 

10  . 

8 

40 

4  2  -  35 

28 

73-61  32 

5 

-  17 

1  1  - 

9 

21 

45  -  36 

12 

64-62  16 

6 

-  21 

12  - 

10 

08 

44  -  36. 

96 

75  -  63  00 

7 

-   25 

13  - 

10 

92 

45  -  37 

80 

76  .  63  84 

n 

-  23 

U  - 

i  1 

76 

46   3o 

64 

77  -  64  68 

9 

'   31 

15  - 

12 

60 

47  -  39 

48 

78-65  52 

m 

-  So 

16  - 

13 

44 

4H  -  40 

32 

79  .  (jC)    36 

11 

-  39 

17  - 

14 

28 

49  -  41 

16 

80  -  67  20 

12 

-  4^ 

18  - 

<5 

12 

50  -  42 

00 

81-08  04 

13 

-  45 

19  - 

15 

\)6 

5i  -  42 

84 

82  -  68  88 

14 

-  49 

20  - 

16 

80 

52  -  43 

68 

83  -  69  72 

3  5 

-  53 

21  - 

17 

64 

53  -  44 

52 

84  -  70  56 

16 

-  b6 

22  - 

18 

48 

54  .  45 

36 

85-71  40 

17 

-  59 

■  23  - 

19 

32 

55  -  46 

20 

86-  72  24 

18 

-  63 

24  - 

20 

16 

56  -  47 

04 

87  -  73  08 

19 

-  67 

25  - 

21 

UO 

57  .  47 

88 

88-  73  92 

20 

-  70 

26  - 

21 

84 

58  -  48 

72 

89  -  74  76 

21 

-  73 

27  - 

i2 

68 

59  -  49 

56 

90  -  75  60 

2^2 

-  77 

28  - 

23 

52 

60  -  50 

40 

91  -  76  44 

23 

-  81 

29  - 

24 

36 

61  -  51 

24 

92  -  77  28 

24 

-  81 

3J  - 

^25 

20 

62  -  52 

08 

93-73  12 

M   - 

26 

26 

t'4 

63  -  52 

92 

94  -  78  96 

cf-^^. 

dls.  cts. 

32  - 

88 

64  -  53 

76 

95  -  79  80 

1  - 

84 

33  - 

27 

no 

65  -  54 

60 

96  -  80  64 

2  - 

I  68 

34  - 

28 

56 

66  -  55 

44 

97  -  81  48 

3  - 

2  52 

35  - 

?9 

40 

67  -  56 

28 

93  -  ;^2  32 

4  - 

3  36 

36  - 

30 

24 

68  -  57 

12 

99-83  16 

5  - 

i  20 

31   - 

31 

08 

69  -  57 

96 

100-84  00 

C  - 

5  04  i 

38  . 

31 

92 

' 

Note. — The  Act  of  Congress,  on  which  the  foregoing  tables  were 
onlculated,  expired  oa  the  iirst  Nov.  1819,  when  all  forei^a  Gold 
Cain4  cca&ed  Xq  be  a  lawful  tender. 


MERCANTILE  PRECEDENTS.  249 

MERCANTILE   PllECEDEiNTS. 


BILL  OF  EXCHANGE, 

Sahnu  September   12,   1822. 
EXCHANGE  for  £1000  sterling. 

At  twenty  days  sight  oi'this  my  first  of  exchange  (second 
and  third  of  the  sanrie  tenor  and  date  not  |)al(l)  pay  to  John 
P-arker,  or  order,  one  thousand  pounds  sterling,  with  or  witit* 
#ut  further  advice  from 

Your  humble  servant, 
WILLIAM  P£ABODY. 
Messrs.  Button  Si  Green, 
Merchants, 

London. 


BILL  OF  GOODS, 

At  an  advance  on  the   sterling  cost. 

Boston^  Oct.  5,  1822. 
Mr.  William  Poole 

Bought  of  Simon  Simmonds, 

32  ells  Mode         -         -       Is.  Sd.  steri.  £2     13     4 

64  yds.  striped  Nankins       \s.  Od.         -  -      4      16     0 

28  do.  striped  Calico     -       \s    dd.         -         -       2       9      0 

4  pieces  K\issel  .     -         24*.  -         -      4      IG     0 


Sterling     14      14     4 
Exchanf;e,   331-  per  cent.       '^     ^^      U 


£19      12     bi 
Advance  at  20  per  cent.         3     18     5^ 

£23     10   11 


Dollars     73,43 

Received  bis  note  at  2  months, 

Simon  Sjmmonds. 


250  MERrANTlLE  PRECEDENTS. 

PROMISSORY  JVOTE. 

Boston.,  Oct.  5,  1822.     For  value    received  I  promise    t« 
pay  to  Simon  Simmoiuis,  or  order,  seventy  eight  dollars  for- 
ty eight  cents,  on  demand,  with  mterest  alter  two  months. 
Attest.  William  Foole. 

Saul  Jamec. 


A  RECEIPT  FOR  AjY  ENDORSEMENT  ON  A  NOTE. 

Boston,  Dec.  12,  1822.  Received  from  Mr.  William  Poole, 
(by  the  hands  of  Mr.  Betijamin  Flint)  thirty  eight  dollars^ 
seventy  cents,  which  is  endorsed  on  his  note  of  Oct.  5,  1822. 

Simon  jjimmonds. 

38  dolls.  70  cts. 


RECEIP  T  FOR  MONE  Y  RECEIVED  ON  ACCOUNT. 

Boston.^  January  10,  1804.  Received  from  Mr.  D.  Evan?, 
(by  the  hands  of  Mr.  l  homus  Dunmore)  four  hundred  ani 
thirty  dollars  on  account.  Geokgi!:  Page. 

43u  dolls. 


PROMISSORY  NOTE  BY  TWO  PERSONS. 

Salem.,  July  12,  1822.     For  value  received  we  jointly  and 
{»everaily  promise  to  pay  to  Mr.  Samuel  Rich,  or  order,  five 
hundred  dollars  fifty  four  cents,  on  demand,  with  interest. 
Attest  Nathan  Say  born, 

William  Boltox.  Stlfhen  Needy. 


GENERAL  RECEIPT. 

Nexi^- Bedford^  March  27,  1822.     Received  from  Mr.  N.  B, 
I'he  st,:n  (.itrn  ^l-l'ars  twenty  nine  cts.  iatuii  of  all  demands. 
10  doiis.  29  ct.«.  E.  D. 


MERCANTILE  PRECEDENTS.  251 

BILL  OF  PARCELS. 

Salem^  June  20^  1804. 


Mr.  William  Holman 


Bought  q/*  Daniel  Green, 


1  hhds.  sugar, 

wt 

viz. 

C. 

q.       lb. 

C.    9.       /^r. 

No.   1. 

5 

2        7 

No.   5. 

5     3      19 

2. 

5 

1      22 

6. 

5      I      07 

3. 

6 

0      13 

7. 

5      1      07 

4. 

5 

2      13 

8. 

5     3      14 

22  2  27 

22  2        1 

45  I        0 

Tare  1 2 per cwt.  4  3  IT 


22     2       1 


Neat  40     I      17  at  12  dolls,  per  cwt. 
2  bbls.  sugar,  viz. 


dolls,  cts. 
484     82 


a 

2 
I 

q,      lb. 

2  25 

3  17 

Tare  21  lb.  per  bbl 

4 
4 

viz. 

2      14 
1      U 

Neat 
3     hhds.    molasses, 

1        0  at  10  dolls. 

galls. 
101-9* 
ion— 5 
107—7 

316-21 
21 

-      42     5© 


295  ^allon5»  at  50  cK  -  147  5« 
1  quarter  cask  Mahira  wirio  -  25  00 
5  cases  gin,  at  4  dolls.  25  cts  -     21     25 


dolU.  721  07 


*  The  ullage  is  thus  noted. 


^52  MERCANTILE  PRECEDENTS, 

LYFOICES. 

Invoice    of  20    hhds.  clayed  suoar  and    10    hhds.    coffee, 

shipped  by of  Boston,  in  the  United  SU\tos  of  America^ 

on  his  own  account  and  risk,  on  board  the  ship A  B 

master,  bound    for and  a    market,  consigned  to    the 

said  A  B  for  sales  and  return:^,  viz. 
50  hhd?    clayed  sugar,  viz. 

B.  C.        No.  C.  q.  lb.  No.  C.  q,  lb. 

No.   1  a  20      I.  113    14  11.  Vl  0    !4 

2.  10  3   "21  12.  10   ^Z   U 

3.  110    0  13.  10  2   21 

4.  12    10  14.  113   21 

5.  11    1   14  15.  10   I    14 

6.  10  3     7  16.  10  2    0 

7.  10  2     0  17.  11    2  21 

8.  110    7  18.  10    I    14 

9.  II    0  21  ^  19.  1117 
10.               10  0     7              20.               10  3    14 


111 
no 

0  7 
2    0 

221 
23 

2    7 

2  27 

110  2    0 


Care  12  per  cwt. 

dolU.  cts. 

197  3     8  neat,  at  10  d.  25c.  2u2 7  67 
10  hhds.  coffee,  \vt.   viz. 

B.  C. "     No.       C.  q.    lb.   Ta-e.     No.  C.  q.  'b.   Tare. 

1^0.   I.  a  40     I  9  2       7     i08         6.  6   I     14     79 

2.  9    3      0      12         7.  6   1       6     CI 

3.  10  I  21  '06  8.  8  2  4  84 
4  10  2  14  i03  9.  9  I  8  91 
».         8    0     14       94       10.  10  0    14     108 


48    2      0     523  40  2    18    428 

40    2    18     423 

946 

8.0  0    lS=9986j^ 
deduct  tare     946 

9010  Ib.neat,  at  21  cts.  1898  4f 

3926  07 

Premi'im  of  iiT^nring  4176  dolls.  67  cts.  at  6  per7             250  69 
cent,    o  <o/er  the  amount         -         -         -       J _^ 

Btfstotiy  kc,  dolls.  4176  66 


MERCANTILE   PRECEDENTS. 


263 


IXVOICE, 


Invoice  of  merchandise  on  board  the  brig  Swan,  A.  B.  ma<?- 
ter,  shipped  by  A.  M.  on  his  own  account  and  risk,  for  the 
AVest-lndies,  and  consigned  to  said  master  for  sales  and    re- 


turns,  VIZ.                                                      dolls. 

dolls. 

140  M.  boards  and  piank, 

10 

1400 

20  M   white-oak  hhd.  staves 

i30 

600 

12  M.  red-oak  hhd.          do. 

12 

144 

130  M.  shingles 

3 

390 

B.  No.  1-18.  18  hhds.  of  cod-fish,  17303  lb.  4  pr. 

C.  692 

12 

B    No.  1-52.52  bbls.  of  beef      -       - 

12 

624 

E.  No.  1-30.  30  bbls.  of  salmon  -      - 

10 

300 

F.  No.  1-2.    2  bbls.  pork      -     -      - 

18 

36 

L.  No.  1 — 7-    7  casks  of  rice,  neat      } 
39  C.  3  qrs.  21  lb.      \ 

4  pr. 

C.  159 

7» 

3     M.   of  hoops 

25 

75 

1300  pair   of   shoes 

50  cts.  6^0 

5a/«m,  Sept.  7,  1822. 

Errors  excepted. 


dolls.     5070     87 


A.  M. 


Jl/r.   Mraham  J&nen  to  Walter  Brown^ 
182^. 

For  1  barrel  of  flour 
4  Ih.  coffee 
9  lb.  of  sugar     - 
7  gallons  of  molasses 
3  quintals  of  tish 
2  lb.  hyson  tea 
b  lb  chocolate 
2  bushels  of  corn 


Errors  excepted. 


Dr. 


May 

5. 

8. 

9. 

23. 

June 

7. 

16. 

July 

25, 

Aug^. 

5. 

-      dolls. 

10 

2*. 

1   3S 

11^. 

1   37 

3*.  9fZ. 

4  37 

15^. 

7  50 

8.9.  bd. 

2  83 

Is,  6d. 

1    25 

4s,  Od. 

1    53 

dolls. 

30  23 

z 


:^51 


MERCANTILE  PRECEDENTS. 


.^CCOUATS  OF  SfiLES, 

SALES  c/20  hhch.  7  hhls.  arJ  31  hags  Coffee,  for  and  on  risk 
of  AW.   Jl  ill  lain  Sn/hnan,  la-'rchant.  in  Portland. 

1S22. 

March  16.      VrilJiam  Ede-,  20  bLds.  wt.  14376  lb  > 

at  23  cts.  per  lb.  \  ^^^^^-  3S06  48 

16.  George  Watts,  7  bbls.  wt.  1943  lb.  at  23  cts.  843  Z9 

17.  Peler  Bates,  3i  bags,    '*     5507  23  cts.  1266  61 


Charges. 

Ad/ertising  .         -         -         -  dolls.      1   .^^0 

Storage        -  .         -         -  .  3   rg 

Commission  on  4916  dolls.  48  cts.  at  2i 
per  cent. 


491G  48 


Neat  proceeds  passed  to  hi-  credit. 
Errors  excepted,  &c. 


122  91  127  91 

dolls.  4788  67 


SALES  of  sundry  inerchani'ise  received  per  ship  Juno.,  Cant. 
Dane  from  A'lachias.  and  disposed  of  for  account  and  risk 
of  Amos  Goodwin.,  mcrrJiant^  there. 


Date,  j  To  whom  sold. 

barrels  oil 
bbls.  salmon 
bbls.  herring 
cords  wood 
cords  bark 

feet  boards 
barrels  beef 

PHce. 

o 

1 

1822 

dls.cts. 

dh.  cts. 

June  4     James  Yates 

SO 

3               90 

8  1  Wm.  Roc 

120 

3  27      292  40 

27  '  John  Pavson 

6 

12 

72 

July  4     James  Nugent 

22 

4 

88 

-     Cash 

50 

S  75 

437  50 

8  [  Simon  Sai  dri 

3,216 

6  50 

20  90 

21     Stock 

16 

9 

135 

29     Pnvil  Sim-on 

13      1 

3  50 

45   50 

^uo.    S     Jona.  Ho  e 

1,259 

6 

7  55 

Taken  to  fill  '^p 

J 

— 

*~ 

1 50    7  .50 

13 

22 

4,475 

.5 

I28S  85 

Remaining  unsold,  40  barrels  of  herring. 
Charges i  viz. 
Storage  of  fish dolls.  10  50 

Commission  on  1288  dolls.  85  cts.  at  2|  per  cent.        32  22 

^eat  procecdr,  carried  to  the  credit  of  liis  account,  dolls.   1248  IS 

Errors  excepted,  &c 


42  72 


MERCANTILE  PRECEDENTS. 


255 


S.ILFIS  of  19  fih.Js.  an  I  7  bhh.  of  ruin^  receiver!  per  brig  Ruhy^ 
John,  Butler  master^  from  Portland^  for  account  end  risk  of 
Daniel  E'kvards^  merchant^  there. 


" 

.  ) 



— 

ii 

§ 

<C 

■^ 

Date. 

To  whom  sold. 

4  ^ 

5 

,    Contents. 

s 

o 

fi; 

S 
^ 

^i*^ 

1822 

i       1 

Ch.                                               1 

dls.  Ct8. 

Sep.  21 

By  Walter  King            l|     20^100 

29  5§ 

June  2 

By  David  Jones      2 

216  |100 

110  &  lOG 

2?6 

20  1  By  Jamas  Ray         4 

438  i  96 

lO^llO,  IH,I09 

420  48 

24  !  By  Aaron  Jadr^on 

3      81      95 

26^,  27i,  27 

76  9.5 

July  2  5  1  By  John  Davis        1 

115      95^ 

109  82 

Au-.  3  !  By  Parsons &Ely I 

1       25      95i                                1 

23  87 

23  1  By  Simon  Sands  !   2 

222  1  98 

109,  113 

217  56 

Oct.    4  1  By  Moses  Young    1 

1    138  j  06 

1»0,  2S 

132  48 

10      By  Isaac  Black    ]   3 

l]  342i   99  1 

107,101,  103,  28^ 

339  07 

25 

By  Amos  Danda  | 

6 

1 

632  1 

98^ 

109,  102,  106,  }  1 

[191  7  2239  1         jUl,  112,  92 


|_662  5^ 
'12188  25 


Charges. 

Paid  Capt.  Butler  freight  of  19  hhds.  rum,  at 
ditto  -  7  bbls. 

Porterage  19  hhds.         -         -         -         . 

do.         7  bbls.     -         -         -         . 
Gauging  26  casks 


dh.cts. 
2  50 

40 
10 
V2h 


Cooperage  3  dls.  oa  hhds.  1  dl.  50  cts.  on  bbls. 
Advertising  ------ 

Commission  on  2188  dolls.  25  cts.  at  5  per  cent. 


Neat  proceeds 

Outstanding  in  hands  of  dolls,  cts. 

Moses  Young         -         -         339  07 
Amos  Dundas        -         -         622  52 
Salem^  Sept.  2'2.  1829. 

Errors  excepted,  &e. 


dls.  cts. 
47  50 

4  62 

7  60 
70 

3  25 

4  50 
1  50 

106  41 
179  0$ 

dollF.  2009  17 


256  MERCANTILE  PRECEDENTS. 

SALi^S  of  the  Ship  Hiram'' s  Cargo ^  by  William  Sutton, 


1S21.  lb.       Uv.  Hv.  sol. den.  liv.sol.den. 

SJep.24.  65hds.fish,  wt.  neat  72587  at  33  pr  100  23953  14  2 

6   do.         6515   32  do.   2084  16  0 

2   do.         2  5  36   31  do.    662  3  2 

34   do.        366.58   30  do.   10997  8  0 

2      do.  part.  dam.    2 i 84  sold  at  auc.  for  226     0  0 

37924     1     4 

Uv.  sol.  den. 


109 


24  bbls.  beef,   at  101      1     3  per  bbl. 

2425 

10 

0 

7         do.               99     8      5       do. 

697 

'18 

11 

29         do.               90  15     0       do. 

2631 

15 

0 

4         do.               83     0     0       do. 

333 

0 

0 

— 

—  60S8 

8 

11 

64                                      Hv.  sol. 

13  bbls.  pork         -         -       136     0 

1768 

0 

0 

25  do.     porter      -          -          SO     0 

2000 

0 

0 

3  boxes  linen,  cont.  169  ps.  96     0  per  ps. 

16224 

0 

0 

14  firkins  butter,  wt.  1129  lb.   2     5  per  lb. 

2540 

5 

0 

^  thousand  hoops         -          240        per  M 

1200 

0 

0 

59     do.       shiDgles                  16           do. 

944 

0 

0 

15949  feet  boards      -       -     120           do. 

1913 

17 

7 

170  shook  hogsheads       -        8i  per  hhd. 

1402 

10 

0 

—27992 

12 

7 

Uv.     s.     d. 

72004 

17 

10 

Commission  on  72004  17  10,  at  5  per 

cent. 

li^ 

3600 

4 

10 

V.  68403 

13 

0 

Errors  excepted,.  &c. 

Disbursements^  Duties^  <J^'C.  paid  on  ship  liiram.^  by  IVm.  Sutti 

on. 

1822. 

Uv. 

s. 

d      Uv. 

s. 

d. 

Sept.  18.  Paid  for  a  barrel  of  flour 

-       86 

10 

0 

to  the  admiralty 

240 

11 

6 

for  fresh  meat 

-       56 

12 

5 

for  flats  to  unload  with 

341 

13 

6     725 
4 

7 

5 

Paid  to  the  harbour  master 

-       66 

10 

for  storaj^e  and  negro  hire     - 

619 

14 

S 

for  inward  duties 

-      714 

11 

7 

for  outward  duties 

229 

13 

5 

leso 

10 

0 

•  Paid  for  brokerage 

-      821 

13 

6 

for  passport  and  certificate 

68 

19 

7 

—     890 

13 

1 

Ffiint  Pctre,  Guadalonpe,  JYov   ]  2,  1822  liv.     3246   10     (i 

Errors  excepted,  &c. 

WILLIAM  SUTTON.. 


MERCANTILE  PRECEDENTS. 


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258 


xAIERCANTILE    PRECEDRNTS. 


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MERCANTILE  PRECEDENTS. 


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MERCANTILE  PRECEDENTS. 


Dr. 


Mr.   Thomas  Gibson^  in  Interest 


(lis.  cts.  days.  dls.  cts. 

35  00  fr.  Jan  31, '22,  to  Oct.  12,'2i!,256      1    47 


on 


To  Int 

To  do.  on  2962  00  Feb.     2, 

To  do.  on  2590  42  May    31, 

To  do.  on  1733  97  July     2, 

To  do.  on       73  63  July   12, 

To  do.  on    455  52  Aug.  25, 

To  do.  on    15871  Sept.  30, 


do. 

254 

123  68 

do. 

134 

57   Oft 

do. 

102 

29  07 

do. 

92 

1    11 

do. 

47 

S  51 

do. 

12 

0  31 

dolls. 

216  21 

Dr, 

Mr.    William  Mace.^  in  Interest 

1321. 

dolls,  cts. 

?/• 

m.  d. 

dls.    cts. 

March  3. 

To  Interest 

on  3869  20  for 

1 

5     11 

338  97 

April  26. 

do. 

on     273     6    ' 

1 

3    18 

21   29 

Aug.   18. 

do. 

on     400          ' 

11     26 

23  73 

Dec.  28. 

do. 

on     414     6    ' 

7     16 

15  59 

'22Ja.l5. 

do. 

on     200           ' 

7       9 

7  30 

Feb.   19. 

do. 

on     300           ' 

5     25 

8  75 

Mar.  2xj, 

do. 

on   1300          ^ 

4     18  , 
dolls. 

29  90 

442  53 

MERCANTILE    PRECEDENTS.  261 


Account  with  Thomas  Merchant.  Or. 


dolU.                                                              daifs.   dlls. 

cts. 

By  rut 

on  500     fr.  Apr.  24,  '22,  to  Oct.  1  2,  '22,  171      14 

5 

liy  do. 

11.53  25     '        25,               i\o.    !2,          170      .31 

67 

By  do. 

296  24     May  J,               do.    12,          1G2         7 

88 

By  do. 

215            '          5,              do.    12,          160        5 

65 

By  do. 

215  80     June  9,              do.    12,          125        4 

4,5 

hy  do. 

109  74,    '       24,              do.    12,          110         2 

0 

By  do. 

517  90    July  20,              d.).    12,             84        7 

15 

Balance 

;  due  oil  this  ac't  carried  to  the  debit  of  ac't.   1 43 

43 

doll?.21G 

'Si 

Salem^  Sic. 


Aceount  wich  Thomas'  McrcJiant.  Cr. 

1822.  dolls,   cts.  dt^lls.  cts. 

Jan.   16.         By  interest  on     339     67 

427  •  81 


-  y.  m.  d. 


7(37-  -48  _  e  jo^  05     30 

Balance  carried  to  account  current      -      -       417     21 


dolls.        442     53 
Salem^  September  26,  1822 

Erroi-s  excepted, 

THOMAS  MERCHANT. 


262  MERCAXTILK  PRECEDENTS. 

BILL  OF    SILE. 

To  all  people  to  whom  t\.i<  preseat  Bill  of  Sale  shall  come,  I.  R.  P. 
of  Silem,  1.1  the  Sla'e  of  vlassacha^etr-*,  merchdiit,  seijcl  greeting. 
KNOW  iK,  That  I,  the  f^aid  il.   P.   for  and  in  consideratioa  of tl  e  sum 

of  THRE^    THOUSAND  TWO  HUNDRED    AND  TWEN  T  Y-TVVO  DOLLARS, 

to  me  in  liand  well  and  Tuly  paid  at  or  before  the  eiisealing  and  delivery 
of  these  presents,  by  S.  T.  of  the  said  Salem,  merchant,  tl  e  receipt 
whereof  I  do  hereby  acknowledge,  and  am  therewith  f  illy  and  entirely 
satisfied  and  conten  ed,  have  granied,  ban^ained  and  sold,  and  by  these 
presents  do  grant,  bargain  and  sell  unto  rhe  said  S.  T  all  the  hull  or 
body  of  the  good  brig  Sally,  together  with  all  and  singular  her  masts, 
spars,  sails,  rigging,  cables,  anchors,  boats  and  appurtenances,  now  ly- 
ing at  Salem,  and  registered  at  the  port  of  Salem,  the  certificate  of  whose 
registry  is  as  follows  : 

In  p  irsuance  of  an  Act  of  the  Congress  of  the  United  States  of  A- 
merica,  endiled,  "  AN  ACT  concerning  the  registering  and  recording  of 
ships  or  '.  essels,  "  R.  P.  of  Salem,  in  the  State  of  Massachusetts,  merch- 
ant, having  taken  or  subscribed  the  oath  reqired  by  the  said  act,  and 
having  sworn  he  is  the  o  ily  owner  of  the  ship  or  vessel  called  the  Sallv, 
of  Salem,  whereof  William  Knapp  is  at  present  master,  and  i.5a  citizen  of 
the  Uni<cd  S'-.ue^,  as  he  halh  sworn,  and  that  the  said  ship  or  vessel  was 
built  at  Sali-b'iry,  m  the  said  stale,  in  the  year  eighteen  hundred  and 
twenty  o.ie,  as  also  appears  by  a  certificaie  of  enrollment.  No.  129, 
issued  in  this  district  on  the  fourth  day  of  August  last,  now  surrendered — 
and  N.  S  surveyor  of  tIJ.i  di:>>ric^  having  certified  that  the  said  ship  or 
vessel  has  one  deck  and  tw^o  masis,  and  that  her  length  is  sixtynine  feet 
five  inche--,  her  breadth  twenty-tvvo  feet  and  one  half  inch,  her  depth 
eiglit  feet  two  inches,  and  that  she  measures  one  hujidred  and  six  tons 
and  forty  ninety-fifths,  that  she  i,  a  square-s^erned  brig,  has  no  galleries 
and  no  fi'ure  heid,  and  the  said  R.  P.  leaving  agreed  to  the  description 
a:  d  admeasarement  above  speciiied,  and  sufficient  security  having  been 
i:iv  en  according  to  the  said  act,  the  said  brig  has  been  duly  registered  at 
the  port  of  Salem. 

Given  under  my  hand  and  seal  at  the  jjort  of  Salem^  this  sixth  day  of" 
September^  in  the  year  eighteen  hundred  and  twenty  two. 
To  have  and  to  hold  the  said  granted  and  bargained  brig  Sally  and 
premises  with  the  appurtenances  unto  the  said  S.  T.  his  heirs,  executors, 
administrators  or  as  igns,  to  his  only  proper  use,  benefit  and  behoof  for- 
ever. And  I  the  said  R.  P.  do  avouch  myself  to  be  the  true  and  lawful 
owner  of  the  said  brig  and  appurtenances,  and  have  in  myself  fall  power, 
good  right  and  lawful  authority  to  dispose  of  the  said  brig  as  afores-aid, 
and  her  appurteiiances  in  manner  as  aforesaid,  and  furthermore  I  the  Kaid 
R.  P.  do  hereby  covenant  and  agree  to  warrant  and  defend-the  said  brig 
and  premises,  wdth  the  appurtenances  against  the  lawful  claims  and  de- 
mands of  all  per-ons  whatsoever  unto  the  said  S.  T.  In  witness  where- 
of,  I  the  8?iid  R.  P.  have  hereunto  set  my  hand  and  seal,  thishrst  day  of 
September,  in  the  year  of  our  Lord  one  thousand  eight  hundred  and  tweu- 
t^-two. 


MERCANTfLE   PRECEDENTS.  $63 

CHARTER-PARTY. 

THIS  Charter-party  of  affieii^htment.  indented,  made  and 
fally  concluded  upon  this  ninth  ^^y  of  Sej)teniber,  in  the 
year  of  our  Lord,  one  thousand  eight  hundred  and  twenty- 
two,  hetween  J.  P.  of  Salem,  in  the  county  of  Essex,  and 
Commonwealth  of  Massachusetts,  merchant,  owner  of  the 
good  shfp  Ifelen,  of  the  burden  of  two  hundred  tons,  or 
thereabouts,  now  lying  in  the  harbour  of  Salem,  whereof 
11.  S.  is  at  present  master,  on  the  one  part,  and  C.  D.  ot  said 
Salem,  mercliant,  on  the  other  part,  Wiinesseth^  ^\  hat  the 
said  J.  P.  for  the  consideration  liereafter  mentioned,  huh 
lettento  freight  the  aforesaid  ship,  with  the  appurten.uices 
to  her  belonging,  lor  a  voyagf^  to  be  made  by  the  said  sliip 
to  London,  where  sh«»  is  to  be  discharged  (the  danger  of  the 
seas  excepted;)  and  the  said  J.  P.  doth  by  these  {)resents 
covenant  and  agree  with  the  said  C.  I),  in  manner  following, 
That  is  ^'>  5rt//,  that  tiie  said  ship  in  and  during  the  voyage 
aforesaid, shall  be  tight,  staunch  and  strong,  and  sufhciently 
tackled  and  apparelled  with  all  things  necessary  for  such  a 
vessel  and  voyage,  and  that  it  shall  and  may  be  lawful  for 
the  said  C.  D,  his  agents  or  frjctors,  as  well  at  London  as  at 
Salem,  to  load  and  put  on  board  the  said  ship,  loading  of 
such  goods  and  merchandise  as  they  shall  think  proper,  con- 
traband goods  excepted. 

IN  consideraion  whereof,  the  said  C.  D.  doth  by  these 
presents,  agree  with  the  said  J.  P.  well  and  truly  to  pay,  or 
cause  to  be  paid  unto  him,  in  full  for  the  freight  or  hire  of 
said  ship  and  appurtenances,  the  sun)  of  three  dollars  per 
ton,  per  calendar  month,  and  so  in  prop  rtion  for  a  less  time, 
as  the  said  ship  shall  be  continued  in  the  aforesaid  service, 
in  sixty  days  after  her  return  to  Salem.  And  the  said  C.  D. 
doth  agree  to  pay  the  charge  of  victualling  and  manning 
said  ship,  and  all  port  charges  and  pilotfige  during  said  voy- 
age, and  to  deliver  the  said  shi[),  on  her  return  to  Salem,  (o 
the  owner  aforesaid  or  his  order.  And  to  the  true  and  faith 
ful  of  all  and  singular  the  covenants,  paym^Mit^  and  agree- 
ment^ aforementioned,  each  of  the  parties  aforenamed  binds 
and  obliges  himself,  his  executors  and  administrators,  in  the 
penal  sum  of  two  thousand  dollars  firmly  by  these  presents. 
In  witness  whereof,  the  parties  aforesaid  have  hereunto  in- 
terchangeably set  their  hands  and  seals  the  day  and  year 
afore-written. 


264  MERCANTILE  PRECEDENTS. 

BILL  OF  LADLXG. 

SHIPPED   in    orood  order  and  well  con- 

J.  R.  ditioned    by    John    Roily,   in  and  upon  the 

1    a  53         good  ship  called  the  Iris,  whereof  is    nias- 

Casks  Potash^    tor    for  this   present    voyage  Charles  i'ly, 

ton.  cwt.  and  now  ridln?^  at  anchor  in  the  harbour  of 

8       18     £  5.  f^.  Salem  and    found    for    EiverpooK    to    say, 

at  HOs — 35  12  0 fifty   three  cash    of  potash.;  contawins  eight 

Primage  I07is    and    eighteen    czvt     beinsr  mark<^d    and 

5 per  cent.  115  7  numbered    as  in  the   margin,  and  are  to  he 

delivered    in    the  like  good  order  an<l  well 

£37  7  7  conditioned,  at  the  aforesaid  port  of  Liver- 
pool  (the  danger  of  the  seas  excepted)  un- 
to Mr.  J.  Mav  or  to  his  assigns,  they  paying 
freight  fc^r  tlie  said  goods.  /r?;r  pouru's  Lril- 
isb  sterling  per  ton^  With  live  per  cent  prim- 
age. In  witness  whereof  the  master  or 
purser  of  the  said  ship  hath  affirmed  to 
three  bills  of  lading  all  of  this  tenor  and 
date,  the  one  of  v.'hich  being  accomj)lisfied. 
the  other  two  to  stand  void.  Dated  in  Sa- 
lem, Sept.   nth,    1822.  C.  ELY. 


A  NEW 

INTRODUCTION 

TO 

BOOK-KEEPING, 

AFTER    THE 

ITALIAN  METHOD, 

BY 

DEBTOR  AND    CREDITOR : 

m    WHICH  THE  TIIEOny  OF  THAT  ART  IS     NOT     ONLY     ELUCIDATED, 

BUT     THE  PRACTICE  MADE  EASY  AND    FAMILIAR,  BY 

THE  ADDITION  OF   A 


gW  W  3l®©]£^i 


3XniBITING    THE     VARIOUS  INCIDENTS  WHICH  USUALLY  FALL     IN  A 

COURSE  OF  BUSINESS. 

THE     WHOLE    LAID  DOWN  IN  A  MANNER  SO  EASY  AND     INTELLIGIBLE 

AS    TO  BE  UNDERSTOOD  IN  A  FEW    DAYS. 

WITH    A 

WASTE  BOOK 

SUBJOINED  AS  AN  EXAMPLE  FOR  Pr.ACTICE. 

AND     ALL  THE    ACCOUNTS  ARE    REDUCED  TO  THE     FEDEr 

RAL  CURRENCY. 

ON  THE  PLAN  OF   R.  TURNER,  LL.  D. 

Revised  and  Improved  by  a  Merchant, 

Deliver  all  things  in  number  and  weight,  and  put  all  in  wRixiNe 
that  thou  GivEST  out  or  receivest  in.  I  cclus.  xiii.  5, 

SALEM  : 

PUBLISHED  BY  JAMES  R.  BUFFUM. 
J,  D.  CUSHING,  PRINTER. 

1825,. 


DISTRICT  OF  MASSACHUSETTS,  to  wit : 

District  ClerWs  Office. 

BE  IT  REMEMBERED,  That  on  the  twentieth  day  of  December^ 
A.  D.  1819,  in  the  forty- fourth  3-ear  of  the  Independence  of  the 
United  States  of  America,  Gushing  &  Appleton,  of  the  said  district,  have 
ileposited  in  this  office  the  title  of  a  book,  the  right  whereof  they  claim 
as  proprietors,  in  the  words  following,  to  wit  : 

"  A  new  Introduction  to  Book-Keeping,  after  the  Italian  Method,  by 
Debtor  and  Creditor  ;  in  which  the  theory  of  that  art  is  not  only  elucidat- 
ed, but  the  practice  made  easy  and  familiar  by  the  addition  of  a  Set  of 
Books,  exhibiting  the  various  Incidents  which  usually  fall  in  a  course  of 
business  The  whole  laid  down  in  a  manner  so  easy  and  intelligible  as  to 
be  understood  in  a  few  da3^s.  With  a  Waste  Book  subjoined  as  an  ex- 
ample for  practice.  And  all  the  accounts  are  reduced  to  the  Federal 
Currency.  On  the  plan  of  R  Turner,  LL  D.  Revised  and  improved  by 
a  Merchant.  'Deliver  all  things  in  number  and  weight,  and  put  all  ia 
writing  that  thou  givest  oat  or  receivest  in."         Ecclus  xiii  5" 

In  conformity  to  the  act  of  the  Congress  of  the  United  States,  entitled, 
"  An  Act  for  the  encouragement  of  learning,  by  securing  the  copies  of 
maps,  charts  and  books,  to  the  authors  and  proprietors  of  such  copies, 
during  the  times  therein  mentioned  ;"  and  also  to  an  act,  entitled  *'  An 
Act,-  supplementary  to  an  act,  entitled,  '*  An  Act  for  the  encouragement 
of  learning  by  securing  the  copies  of  maps,  charts,  and  books,  to  the  auth- 
ors and  proprietors  of  such  copies  during  the  times  therein  mentioned,  and 
extending,  the  benefits  thereof  to  the  arts  of  designing,  engraving,  and 
etching:  histtrical  and  other  prints*" 

JNO.  W.  DAVIS, 
Clerk  of  the  District  of  Massachusetts, 


BOOK-KEEPING, 


ACCORDING    TO    THE 


ITALIAN  METHOD. 


THE  books  made  use  of  in  this  way  of  keeping  accompts, 
are  chieflj  tliree,  viz.  the    Waste  Book^  Journal^  and  Ledger. 

Of  the  Waste  Book. 

In  the  Waste  Book,  which  is  ruled  with  a  margin  and  two 
columns  for  dolls,  cis.  is  written  down  every  occurrence  of 
trade,  by  way  of  memorandum,  just  as  it  happens  in  the 
course  of  your  business. 

0/  the  Journal 

The  Journal,  being  ruled  after  the  same  manner,  but  with 
columns  for  the  Dr.  and  CV.  pages  of  the  posting  in  the  Ledg- 
er, is  a  book  in  which  every  case  of  the  Waste  Book  is  more 
methodically  expressed,  with  [)articular  mention  of  the  pro- 
per Debtor,  Creditor,  and  Sum  of  Money,  in  one  line,  and 
the  other  circumstances  of  the  affair  in  another,  or  in  as  ma- 
ny as  are  necessarj^ 

Of  the  Ledger. 

The  Ledger  is  ruled  with  a  column  in  the  margin  for  the 
month  and  the  day,  and  also  with  a  column  for  the  folio,  be- 
fore those  for  dolls,  cts.  This  hook,  as  it  is  the  largest,  so 
it  is   the   most  material,  and   contains  the  particular   staited 


aficompt  of  every  person  you  deal  with,  and  every  commod- 
ity you  trade  in.  Every  accompt  of  this  book  consists  of 
two  parts,  a  Debtor  and  a  Creditor.  If  the  accompt  be  of  a 
person,  the  debtor  side  shows  what  he  owes  yon,  the  credi- 
tor what  you  owe  him.  If  it  be  an  account  of  goods,  the 
debtor  sideshows  what  charges  you  have  been  at  for  them, 
and  the  creditor,  what  returns  they  have  made. 

Note.  For  the  ready  finding  of  any  accompt  in  the  Ledg- 
er, there  must  be  an  alphabet  prefixed,  directing  to  the  folio 
where  the  accompt  itself  is  posted. 

The  first  thing  necessary  to  a  just  method  of  book-keep- 
ing is  an  inventory  of  your  whole  estate  ;  that  is,  an  exact 
and  particular  account  of  all  your  eifects  ;  as  cash,  wares, 
debts,  (Sic.  This  makes  up  your  whole  property,  and  is 
what  we  call  stock. 

Li  entering  the  Inventory^  observe^ 

First.  What  money,  goods  and  wares  you  have  in  posses- 
sion, or  are  owing  to  you;  make  each  particular  aecompt 
debtor  to  slock,  and  stock  creditor  by  each  accompt. 

Seconclhj.  What  3^ou  owe  to  any  person,  make  the  stock 
debtor  for  so  much  to  the  person,  and  the  same  person  cre- 
iJitor  by  stock. 

Thirdly.  What  money  is  owing  to  you,  make  the  person 
owing  debtor,  and  slock  creditor. 

In  entering  or  posting  the  several  articles,  observe  this 
general  rule  : 

WHiatsoever  comes  to  you  is  debtor,  and  when  you  ask  on 
what  account  it  comes  to  you,  the  answer  shows  the  creditor. 
Whatsoever  you  part  with,  or  goes  from  you,  is  creditor; 
when  you  ask  upon  what  account  it  goes  from  you,  the  an- 
swer shows  the  debtor.  Thus,  if  you  buy  1  cwt.  of  cheese 
for  5  dollars,  cheese  comes  to  you,  therefore  cheese  is  debt- 
or, and  cash  goes  from  you,  therefore  cash  is  creditor. 

Non:.     ThM    one  rule  will  ca.  j'^  you  through  tlie   whole 

n,-;  *  ^'^    (;f  book-keeping,  as  is    evident  from    the   following 

->i  of  it  to  every  particular  circumstance  that  usually 

ii;<j)j.»;';»«i  in  trade. 


Entering  Commodities  bought  in. 

First.  What  you  buy  for  ready  money,  that  accompt  is 
debtor,  and  cash  creditor. 

Secondly.  What  you  buy  upon  trust,  that  ^ccompt  is 
debtor,  and  the  person  selling  is  creditor. 

Thirdly.  What  you  buy  for  part  money  and  part  trust,  the 
commodity  is  debtor,  and  6ash  creditor  for  the  sum  paid,  and 
the  person  selling  is  creditor  for  the  rest. 

Fourthly,  What  you  buy,  and  give  your  promissory  note 
for,  the  commodity  is  debtor,  and  the  accompt  o^  JVoUs  or 
Bills  Payable  is  creditor. 

Entering  Commodities  sold  out 

First.  What  you  sell  for  ready  money,  that  accompt  is 
creditor,  and  cash  debtor. 

Secondly.  What  you  sell  upon  trust,  that  accompt  is  cred- 
itor, and  the  person  buying  is  debtor. 

Thirdly,  What  you  sell  for  part  money  and  part  trust,  the 
commodity  is  creditor  for  the  whole  value  ;  and  tor  the 
money,  cash  is  debtor,  and  the  person  buying  is  debtor  for 
the  rest. 

Fourthly.  What  you  sell  for  a  promissory  note,  the  ac- 
compt of  JVotes  or  Bills  Receivable  is  debtor,  and  the  commo- 
dity is  creditor. 

Exchanging^  or  Bartering. 

The  commodity  you  part  with  is  creditor,  and  the  com- 
modity received  is  debtor. 

Borrowing  and  Lending  Cash. 

First.  What  you  lend,  cash  is  creditor,  and  the  person 
borrowing  is  debtor. 

Seco7idly.  What  money  you  borrow,  cash  is  debtor,  and 
the  person  lending  is  creditor. 

Thirdly.  What  you  lend  on  note,  JVotes  or  Bills  Receivable 
acoompt  is  debtor  to  cash. 

Fourthly.  What  you  borrow  on  note,  cash  is  debtor  to 
Xotes  or  Bills  Payable  accompt. 

A  A  2 


On  Bills. 

First.  When  you  draw  a  bill  payable  at  any  time  on  a 
person  that  owes  you  money,  the  person  on  whom  the  bill 
is  drawn  is  creditor,  and  accompt  of  bills  receivable  is  debt- 
or. When,  the  bill  is  paid,  accompt  of  bills  receivable  is 
creditor,  and  cash,  or  the  person  to  whom  the  bill  is  paid,  is 
debtor. 

Secondly.  When  a  person  draws  a  bill  on  you,  payable  at 
a  certain  time,  the  person  that  draws  the  bill  is  debtor,  and 
accompt  of  bills  payable  is  creditor.  VVhen  you  pay  the 
bill,  cash  is  creditor,  and  accompt  of  bills  payable  is  debtor. 

Thirdly.  ^  When  a  person  indebted  to  you  draws  a  bill  on 
a  third  person  to  pay  you  so  much,  and  the  bill  is  accepted, 
the  person  that  draws  the  bill,  or  the  accompt  on  which  the 
money  is  due,  is  creditor,  and  accompt  of  bills  receivable  is 
debtor.  When  you  receive  the  bill,  then  accompt  of  bills 
receivable  is  creditor,  and  cash  debtor. 

On   accidental  Losses^  ProfilSy  and  other   Expenses, 

First.  "What  money  you  gain,  win  or  receive  gratis,  cash 
is  debtor  to  prolit  and  loss,  and  profit  and  loss  creditor  by  its 
value. 

Secondly.  What  money  or  commodity  you  give  away, 
lose,  or  is  spoiled,  kc.  is  creditor,  and  profit  and  loss  is 
debtor,  for  its  value. 

On  Foreign  Trade. 

First.  When  goods  are  sent  to  your  factor  abroad,  make 
the  voyage  debtor,  and  the  goods  creditor. 

Secondly.  When  you  have  advice  that  your  factor  ha<3 
received  the  goods,  then  he  becomes  debtor  to  the  voyage, 
And  the  voyage  creditor.  If  he  gains  by  selling  the  goods, 
rie  becomes  debtor  to  profit  and  loss  on   account  of  the  gain. 

Thirdly.  If  he  returns  the  goods,  he  is  creditor,  and  the 
«r')':"5s  arc  d*'btcr. 


Oil  Household  Expenses. 

What  money  or  commodity  you  make  use  of,  or  is  ?peiit 
ioj^ur  family,  &,c.  is  creditorj  and  profit  and  loss  is  debtor, 
for  its  valu^.         * 

NoTK.  You  mny  erect  an  account  of  household  expenses, 
and  make  it  debtor,  instead  of  prolit  and  loss. 

Note  also,  That  you  never  meddle  with  the  account  of 
cash,  but  when  money  is  either  received  or  paid. 

On  Errors. 

If  you  have  ent?^red  any  thing*  in  your  Ledger  under  a 
wrong  title,  or  any  otherwise  false,  you  must  not  blot  it  out, 
but  make  this  mark  (A^)  in  the  margin  against  it,  and  write 
on  the  contrary  side,  Error  per  contra^  with,  the  sum  against 
it,  with  the  same  mark  in  the  margin;  so  will  the  accompt 
be  right  without  blotting,  as  if  you  had  made  no  such  error 
at  all. 

To  remove  an  accompt  from  one  folio  to    another. 

When  in  your  Ledger  any  accompt  comes  to  the  foot  of 
the  page,  and  there  is  not  room  to  finish  it,  balance  or  close 
up  the  accompt  in  that  place  thus  :  add  up  the  debtor  and 
creditor  sides,  and  subtract  the  lesser  from  the  greater,  and 
make  the  less  debtor  to,  or  creditor  by,  itself,  for  the  dif- 
ference carried  to  such  a  page  ;  so  will  the  account  be  bal- 
anced. Then  turn  to  a  new  pair  of  pages  in  the  Ledger,  and 
put  the  title  of  the  accompt  as  Before,  and  make  it  debtor  to, 
or  creditor  by,  itself,  referring  to  the  folio  of  the  old  ac- 
compt. 

To  balance  the   Ledger, 

V/hen  every  transaction  is  entered  into  the  Ledger  out  of 
the  Journal,  the  next  thing  is  to  balance  your  Ledger,  that 
i«,  to  make  it  even  throughout  the  whole  hook.  To  this 
end  you  must  erect  a  new  accompt  at  th<=»  end,  by  the  title  of 
Balance  Debtor^  per  Contra  Creditor.  To  the  debtor  ot  tliis 
accompt  will  be  brought  all  the  mpney,  goods  and  debts  be- 


long-in^  or  remaining  due  to  you ;  and  on  the   creditor  will 
appear  all  the  iU^bU  you  owe.     By  this,  and  the  accompt  of 
profit  and  loss,  will  all  the  other  accompts  be  ej|^«dV4,aJj|y||^ 
folio  win  a:  manner.  '''V!!".  .^'''    "^^^PP^ 

To  balance  your  Cos^';* *  * ..i'^ 

•-• 

First.  Add  up  the  debtor  and  creditor  side  of  the  first  ac- 
compt, which  is  cash,  and  subtract  the  one  from  the  oiiier  ; 
make  Balance  dehtor  to  Cash  for  the  money  remaining  in 
your  hands,  and  Cash  creditor  by  Balance  for  the  same  sum, 
which  will  make  both  sides  of  the  accompt  eVen. 

Secondly.  For  balancing  goods,  observe,  1st,  When  none 
are  sold,  the  account  is  evened  by  making  Balance  creditor 
for  the  whole  remaining,  at  the  first  cost.  2d,  When  all  are 
sold,  then  the  account  is  balanced  by  charging  it  debtor  to 
protit  and  loss  for  the  gain,  or  creditor  for  the  loss.  3d, 
When  only  part  are  sold,  first  make  the  accompt  creditor  by 
balance  for  what  remains,  at  prime  cost,  and  balance  debtor, 
and  charge  the  ^oods  debtor  to,  or  creditor  by,  profit  and 
loss  for  the  money  gained  or  lost  on  what  are  sold. 

Thirdly.  For  balancing  the  accompts  of  men,  observe,  1st, 
AVhen  the  debtor  side  is  heaviest,  i.  e.  when  they  owe  you 
any  thing,  then  make  their  accompt  creditor  by  balance,  and 
balance  debtor  for  the  sum  remaining.  2d,  When  the  cred- 
itor is  heaviest,  i.  e.  when  you  owe  them,  then  charge  their 
accompt  debtor  to  balance,  and  balance  creditor  by  the  dif- 
ference. 3d,  When  both  sides  are  even,  then  you  are  only 
to  add  the  debtor  and  creditor  sides  together,  and  set  down 
the  same  sum,  and  it  is  done. 

The  last  account  save  two  to  be  balanced  is  Profit  and 
Loss.  Add  up  the  debtor  by  itself,  and  the  creditor  by  itself, 
and  deduct  the  lesser  sum  out  of  the  greater,  and  note  the 
difference;  then,  if  the  debtor  be  more  than  the  creditor, 
make  stock  debtor  for  so  much  lost;  but  if  the  creditor  be 
more  than  the  debtor,  make  stock  creditor  for  so  much 
gained. 

The  last  accompt  to  be  balanced  is  balance  itself.  Add 
up  severally  the  debtor  and  creditor  side,  and  make  the  cred- 
itr  sio^  e<?ual  to  the  debtor,  by  making  balance  creditor  by 


stock,  and  stock  de1)tor  :  then  add  up  (he  debtor  and  credi- 
tor sides  of  the  stock,  and,  if  the  sums  are  equal,  your  ac- 
compt  is  rig-htly  stated ;  otherwise  it  is  wrong,  and  yon 
must  search  till  you  find  out  the  error. 

Of  opening  anew  Set  of  Books. 

The  manner  in  wUich  a  new  inventory  is  to  be  formed 
from  the  said  balance,  in  order  for  opening  new  books,  is 
thus  : — Make  the  particulars  on  the  debtor  side  of  balance, 
being  the  several  branches  of  your  estate,  severally  debtors 
to  stock,  and  stock  creditor  :  and  make  the  particulars 
on  the  creditor  side  of  balance,  being  the  several  debts 
you  owe,  severaTly  creditors  by  stock,  and  stock  debtor. 


ICJ^  It  is  customary  with  merchants  to  distinguish  their  beoks  by  the 
letier.,  of  the  alphabet :  the  first  set  they  mai;k  with  A,  the  second  with 
Bj  the  third  C^  and  &•  on. 


THE 

WASTE-BOOK. 


g^When  you  post  any  account  out  of  a  Waste-Book  intc^ 
the  Journal,  you  must  write  J.  against  it,  in  the  margin,  to 
show  that  that  account  is  Journalized. 


12 


j       Boston^  January    \st^  1819. 


An  Inventory  of  the  Money,  Wares 
and  Debts  belonging  to  me,  A.  B. 

dolls,  cts. 
[  have  in  ready  money  -         1000,00 

10  bags  of  hops,  at  10  dolls,  per  hag  100,00 
4  pipes  of  wine,  at  65^  dolls,  per 

pipe         -         -         -         -  262,00 

6  pieces  of  hroadcloth,  at  90  dolls. 

10  cts.  per  piece         -         -        540,60 
Thomas  Richards  owes  me,  on  de- 
mand -         .         -         -  45,75 


D. 


C. 


1948 


35 


I  am  indebted, 

To  John  Forrest  on  bond 
To  Samuel  Taylor  on  account 


50,00 
10,00 


Bought  of  John  Jones  |  ton  of  Cheshire 
cheese,  at  65,  50  per  ton,  for  which  1 
paid  cash         -         .        -         .        . 


60 


Od 


32 


7ft 


-.3d. 


Bought    of  Richard   Payton  4  hogsheads   of 

cider,  at  10,75  per  hhd, 
Paid  in  cash         -         -         -         -        25,50 
Remains  due  at  1  month      -        -        17,50 


43    0© 


lo 


Boston^  January  5th^  1819. 


Bought  of  Samuel  Taylor  2  hogsheads  of 
tobacco,  at  39,60  per  hhd. — to  pay  in  3 
months 


Sold    to  John  Williams  4  bags  of  hops,    for 
cash,  at    15,75   per    bag 


I   D. 


-7th- 


-10th- 


Sold  to  Samuel  Taylor  2  pipes  of  wine,  at 

80,33  per  pipe  : 
Received  in  cash         -         .         -         50,75 
Ptemains  due  on  demand         -       -    109,91 


■  15th  — 


Sold  John  Jones  1  piece  of  broadcloth,   to 
be  paid  in    1  month         _         -         - 


19th- 


Bartered  4  hhds.  of  cider  at  10,00  per  hhd. 
for  ^  ton  of  Gloucester  cheese,  at  the 
same  valued 


■  22il. 


Lent  Andrew  Thompson,  to  be  paid  on  de- 
mand        ------ 


-  26th  - 


Drawn  a   bill  on  Thomas  Richards,  to    be 
paid  at  sight         -         -         -         - 


79 


160 


97 


40 


20 


20 


C. 


Bb 


14 


Boston^  Jamtary  2JUA,  1819. 


l*homas    Richards   paid    the  bill  which    1 
drew  on  him         -         .         -         - 


-29ih- 


Fohn  Forrest  has  drawn  a  bill  on    me,  pay 
able  at  sight         -         -         -         -         . 


—  February  5lh 


40 


Paid  the  bill  John  Forrest  drew  on  me        |  40 

^, sth 


Borrowed    of  James  Morgan  the  sum  of  40 
dollars         .         -         -         -         . 


— 9th- 


Paid  John  Forrest  a  quarter's  interest,  due 
December  last         -         -         -         _ 


—  lOth- 


This  day    dined    with  the   Hon.  A  B,  Esq 
and  gave  his  servants         .         -         _ 


-llth- 


■^- 


Won  at  billards  this  day 
13th— 


Paid  household  expenses  la^^t  month 


Paid  my  book-keeper  one  quarter's  salary, 
and  other  expenses         "         "         " 


40 


00 


00 


C 

00 

00 
00 

00 


80 


15 


50 


15 


W.C. 


Boston,  February  I6th,  1819. 


Shipped    in  the  America,  John  Lane    mas- 
ter, consigned  to  William   Cowley,  mer 
chmt,    New-York,    marked    as    in    the 
margin, 
2  cwt.  of  Cheshire  cheese,  value        C,75^ 
Paid  treij^ht  and  custom         -         -     2,331 


-20th- 


Received   advice  that  William  Cowley  has 
received  the  cheese  sate  at    New- York  : 
Sold  for         -         .         -         -  21,071 

Charges  deducted         _         -         -      2,75 


-23d- 


Received  from  my  factor,  William  Cowley, 

at  New-York,    1  chest  of  sugar: 
\eat  weights  cwt   2  qr. ;   value        15,87' 
Paid  freight  and  custom  here         -     2,45 


-25tli-. 


Received  a  legacy  lei't  me  by  my  uncle 
27th 


Paid  for  supporting  the  poor 


End  of  the  Waste-Booh. 


D. 


11 


18 


18 


20 


00 


THE 

JOURNAL. 


The  figures  in  the  first  column  of  the  margin  refer  to  the 
foUos  of  the  Ledger  where  the  debtor-accompt  is  found  ;  those 
in  the  second  column  the  creditor-accompt. 


Bb2 


18 


\\ 


Boston,  January  1,  1819. 


Sundry  Accounts  Dr.  to  Stock, 

Cash,  in  ready  money 
Hops,  for  10  bags,  at  10,00  per  bag 
Wine,  for  4  pipes,  at  65,60  per  pipe      - 
Broadcloth,  for  6  piece??,  at  90,10  per  piece 
Thomas  Richards,  due  on  demand 


— " 


Stock  Dr.  to  Sundry  Accounts, 

To  John  Forrest,  on  bond 

To  Samuel  Taylor,  on  account 


t<_ 


Cheese  Dr.  to  Cash, 

For  half  a  ton  of  Cheshire 


-3d- 


Cider  Dr.  to  Sundry  Accounts, 

To  Cash,  paid  in  part  for  4  hhds,  at 

10,  75  per  hhd.         -         -         -       25,50 

To  Richard  Payton,  remains  due  at 

1  month       -         -         ^         -  17,50 


--5th- 


Tobacco  Dr.  to  Samuel  Taylor, 

For  2  hhds,  to  pay  in  3  months,  at  39,60 
per  lihd,  -        -         - 


19 


Boston^  Jamiartj  Ith^  1819 


Cash^r.  to  Hops, 

Received  fur  4  bags,  at  15,75  per  bag 


-lOth- 


Sundry  Accounts  Dr.  to  Wine, 

Cash,  received  in  part  for  2  pipes        50,75 
Samuel  Taylor,  oa  demand,  for    -     109,91 


.15th. 


John  Jones  Dr.  to  Broadcloth, 
For  1  piece,  to  be  paid  in  1  month 

1 9th 


Cheese  Dr.  to  Cider, 

For  4  hhds.  received  in  barter  for  half  a 
ton  of  Gloucester,  of  the  same  value  - 


-22J- 


Andrew  Thompson  Dr.  to  Cash, 

To  be  paid  on  demand         -         -         - 


-  eoth . 


Bills  Receiv^able  Dr.  to  Thomas 
Richards, 

For  one  drawn  on  him  to  be  paid  at  sight 


-2Cth.» 


Cash  Dr.  to  Bills  Receivable, 

Received  the  bill  of  Thomas  Richards 


D. 

63 


e. 

00 


160 


97 


OG 


15 


40 


20 


•00 


00 


20 


00 


20     00 


20 


John  Forrest  Dr.  to  Bills  Payable, 

For  one  to  be  paid  by  me  at  sight 


7 


Boston^  January  20/A,  1819. 


•  Feb.  5- 


Bills  Payable  Dr.  to  Cash, 

Paid  John  Forrest  the  bill 


•8th- 


Cash  Dr.  to  James  Morgan, 

Borrowed  of  him         .         -         - 


•9th- 


Profit  and  Loss  Dr.  to  Cash, 

Paid  John  Forrest  one  quarter's  interest 


-10th- 


Profit  and  Loss  Dr.  to  Cash, 

Given  A  B  Esq's  servants 


llth- 


Cash  Dr.  to  Profit  and  Loss, 

Won  at  billiards         -         -         - 


-13th- 


Profit  and  Loss  Dr.  to  Cash, 

For  one  month's  household  expenses 


-15th- 


Profit  and  Loss  Dr.  to  Cash, 

;\)r  a  quarter's  salary  to  my  book-keeper, 
and  other  expenses. 


21 


Boston,  February  \Wu  1819. 


Voyage  to  New-York  Dr.  to  Sun- 
dry Accounts,  ^. 

To  Cheese,  for  2  cwt.         -         -        B,75^ 
To  Cash,  paid  freight  and  custom  -    2,33i 


..-20th- 


11 


c. 


09 


William  Cowley  Dr.  to  Sundry  Ac- 
counts, 

Fo  Voyage  to  New- York         -         11,09 
To  Profit  and  Loss,  gained  by  selliRg 
Cheese         -         ^         -         -  7,23^ 


3d-. 


Sugar  Dr.  to  Sundry  jV.ccounts, 

To  William  Cowley,  for  1  chest,  neat 

weight  3  cwt.  2  quarters  -       15,07^ 

To  Cash,  paid  freight  and  custom  -    2,45 


-25th- 


Cash  Dr.  to  Profit  and  Loss, 
For  a  legacy  left  rae  by  my  uncle 


10 


32-?r 


-27th- 


Profit  and  Loss  Dr.  to  Cash, 

Paid  for  supporting  the  poor 


End  of  the  Journal. 


18 


20 


00 


32i 


00 


87. 


THE 

LEDGER. 


(f^  Every  entry  in  the  Ledger  must  be  written  double  : 
the  debtor,  or  accompt  charged;  the  creditor,  or  accompt  dis- 
charged ;  so  that  every  debtor  must  have  its  correspondent 
creditor,  and  every  creditor  must  have  its  debtor,  and  each 
of  them  answering  exactly  the  other. 

The  column  placed  before  those  for  dolh.  cts.  on  the  debt- 
or side  is  marked  Cr.  and  refers  to  the  folio  where  the  same 
accompt  has  credit  ;  that  on  the  creditor  side,  marked  Dr. 
refers  in  like  manner  to  the  folio  where  the  same  is  made 
debtor. 

It  may  not  be  improper  to  advise  the  book-keeper,  when 
posting  up  his  accounts  in  the  ledger,  always  in  the  first 
place  to  po?t  up  his  debit,  then  give  the  proper  credit  of 
that  entry  ;  for  if,  through  haste  or  some  interruption,  a  mis- 
take arises  on  the  Cr.  side,  it  is  not  of  such  bad  consequence 
as  when  it  ha[)pens  on  the  Dr.  side;  for  the  one  may  be  a 
total  loss,  when  the  other  is  but  an  error  in  accompt 

Let  tlie  Waste  be  examined  before  Journalizing,  and  the 
Journal  before  postmg. 

Journalize  and  post  in  the  exact  order  in  wJiich  tlie  en- 
tries occur. 


24 


Page 


13 

Broadcloth, 
Bills   receivable. 
Bills  payable, 


Page 

6 
6 


Balance, 

9 

c 

Cash, 
Cheese, 
Cider, 
Cowley  (Wm.) 

1 

-      4 
4 

-    8 

D 

E 

F 

Forrest  (John) 

-    3 

G 

H 

Hop?,     - 

-  C'> 

I 

Jones  (John) 

5 

K 

L 

M 

Morgan  (James) 

^ 

25 


N 

Page 

4 
-  7 

o 

P 

Pay  ton  (Richard) 
Proiit  and  Loss, 

Q 

: 

R 

Richards  (Thomas) 

-     3 

Stock, 
Sugar, 

s 

-     1 

8 

T 

Taylor  (Samuel) 
Tohacco, 
Thompson  (Andrew) 

3 
-   5 

-6 

V^oyage 

V 

to  New-York,  -     8 

w 

Wine, 

2 

X 

Cc 


1819 


26 
Stock  Dr. 


Jan.  1 1  To  Sundry  Accounts  as  per  Journal, 
To  John   Forrest,  on  bond 
To  Sannuel  Taylor,  on  account     - 
To  Balance  for  the  neat  of  my  estate 


Jan 


Feb.  8 


Cash  Dr. 

To  Stock,  in  ready  money 
To  Hops,  received  ior  4  bags 
To  Wine,  received  in  part  for  2  pipes 
To   Bills    Receivable,    received   oi 

Thomas  Richards 
To  Jimies  Morgan,  borrowed  of  b'm 
To  Profit  and  Loss,  won  at  billiards 
To  Profit  and  Loss  ier  a  Icgac}^   ieit 

me  by  my  urclc         -         .         - 


Cr       D. 


50 

10 

1  9 1 5 


1973 


1000 
63 
50 


40 


20 


1201 


1] 


1819 
Jan.  1 


27 

Contra  Cr. 

By  Sundry  Accounts,  as  per  Journal, 

3y  Cash,  in  reaily  money 

By  Hopf?,  10  bags,  at  10,U0    per  bag 

By  Wine,  4  pipes,  at  65,  50  per  pipe 

By  Broadcloth,  6  pieces,  at  90, 10  per 
piece         ----- 

By  Thomas  Richards,  due  on  de- 
mand        -         -         -         ,         ■■ 

By  PrOiit  and  Loss,  gained ^in  trade 


Jan.  1 

3 

22 

Feb.  5 
9 

10 

lo 

15 

13 
23 

97 


I 


Contra  Cr. 

By  Cheese',  paid  tor  half  a  ton 
By  Cider,  paid  in  part  for  4  hhds. 
By  Andrew  Thompson,  lent  him 
By  Bills  Payable,  paid  John  Forrest 
By  Profit  and  Loss,   paid  a  quarter\s 

interest         -         -         -         - 
By  Profit  and  Loss,  given  A  B  Esq's 

servants         -         - 
By  Profit  and  Lo3s,'paid   household 

expenses         -         -         -         - 
By  Profit  and  Loss,    paid    my  book- 
keeper   a    quarter's    salary,    and 
other  expenses         -         -         - 
^y  Voyage  to  N.  York,  p:\idfreight 
and  custom         -         -         -         - 
By  Sugar,  paid  do.         -         -       ,  - 
By    Profit    and    Loss,  paid  for   sup- 
porting the  poor         -         -         - 
By  Balance,  rem^iins  in  my  hand      I 


Df 


D. 

0. 

1000 

00 

100 

00 

262 

00 

510 

60 

45 

75 

24 

G8 

1973 

03 

3^2 

75 

25 

50 

20 

00 

40 

00 

00 

75 

00 
15 


00 
1009 

120 ! 


80 
G7 


r*«2'- 

45 

87,1. 

9.-1 1 


1819 
Jan,  1 


28 
Hops  Dr. 

To  Stock,  10  bags,  at  10,00  per  bag 
To  Profit  and  Loss  gained 


2] 


JatK.  1 


Wine  Dr. 

To  Stock,  4  pipes,  at  65,50  per  pipe    t 
To  Profit  and  Loss,  gained 


^an.  1 


D. 

c. 

100 

00 

23 

00 

123 

00 

262 

00 

29 

66 

Broadcloth  Dr. 


To    Stock,  6  pi<-ce-^,    at  90,10    per 

piece         -         -         -         -         -j    1 
To  Profit  and  Loss,  gamed         ,  7 


291 


66 


640 

7 

M7 


60 
05 

65 


2T 


1819. 
Jan.  ' 


29 
Contra  Cr. 

By  Cash,  received  for  4  bags,  al 
1 5,7.j  per  bag         -         -         - 

By  Balance, reaiain  6  bigs,  at  10,00 
per  bag         -         -         .         _ 


Contra  Cr. 


Jan.  10  By  Sundry  Accounts,  as. per  Journal 
JBy  Cash,  received  in  part  for  2  pipei 
I  By  Samuel  Taylor,  ren)ains  due 
jBy  Balance,  remains  2  pipes 


Jan,  15 


Contra  Cr. 

By  John  Jones,  to  pay  in  1  month 
flBy    Balance,    remain    5    pieces,    al 
90,10  per  piece         -        -         - 


Cc  Ja 


D. 

G. 

G3 

00 

GO 

00 

123 

00 

50 

75 

109 

91 

131 

00 

291 

66 

97 

15 

450 

50 

547 

65 

30 


1819 
Jan.  1 


Ian,  29 


Thomas  Richards  Dr. 

To  Stock  due  on  demand 


John  Forrest  Dr. 

To  Bills  Payable,  for  Qne  drawn  on 

me,  to  pay  at  sight         - 
To  Balance,  remains  due  to  him 


Jan.  10 


Samuel  Taylor  Dr. 


To  Wine,  due  on  demand 


Cr 


45 

45 

C. 

75 

75 

40 
10 

50 

00 

00 

00 

109 
109 

91 
91 

3] 


1819 
Jan.  26 


Jan,  1 


Jan.  1 


31 

Contra  Cr. 

By  Bills  Receivable,  for  one   drawn 

on  him,  to   be  paid  at  sig-ht 
By  Balance,  remains  due  on  demand 


Contra  Cr. 

By  Stock,  due  on  bond 


Contra  Cr. 

By  Stock,  due  on  account 
By  Tobacco,  for  2  hhds. 
By  Balance,  due  me- 


Dr 

D. 

6 

20 

9 

25 

45 

00 

75 

75 


50 


5(» 


00 


00 


10      00 


79 
20 


-^0 
71 


109      91 


1819 
Jan.  1 


32 
Cheese  Dr. 

To  Cash,  paid  for  half  a  ton  of 
Cheshire         _         -         -         - 

To  Cider,  bartered  4  hos-sheads,  at 
10,00  per  hhd.  for  half  a  ton  of 
Gloucester         _         -         - 

To  Profit  and  Loss,  gained 


Dr 


Cider  Dr. 

Jan.  3  To  Cash,  paid  in  part  for  4  hhds. 
I  To  Richard  Pay  ton,  remains  due 

i 


Richard  Payton  Dr. 

Jan.  3jTo  Balance,  re  mains  due  to  him 


[4 


D. 


32 


40 
2 

74 


C. 


00 
20^ 

954 


25      50 
17      50 


43 


00 


50 


4] 


1819 


Contra  Cr. 


Feb,  16 'By  Voyage  to  New-York,  for  2  cvvt, 
orChe««hire         _  -         - 

By  Balance,  n^mains  half  a  ton 
Gloucester 

By  Balance,  remains  8  cwt.  of 
Cheshire         .         .        -         - 


feb.  19 


fan.  3 


Contra  Cr. 

By  Cheese,  half  a  ton  of  Gloucester 
receiverl  in  barter  for  4  hhus.  at 
10,()(>  per  hhrl. 

By  Profit  and  Loss,  lost 


Dr^    D.     I   'W^' 


Contra  Cr, 

By  Cider  remains  due  at  one  month 


40 
26 


20 


74       951. 


40 
3 


00 

00 


13  I    00 


4         17 


50 


1810 
Jan.  5 


34 
Tobacco  Dr. 

To    Samuel  Taylor,  for  2  hhds.    toj 
be  paid  in  3  months 


Jan.  15 


John  Jones  Dr. 

To  Broadcloth,  for  1  piece,    to  pay 
in  one  month 


Note.     The  Debtor  side    of  all   accompts 

of  goodSi   shows   wliat   they    cost ;  the 

Creditor   sidej   what  returns  they   have 

^ipade. 

Note  also,  That  the  Debtor  side  of  all 
accomps  of  nun.,  m  the  charge,  or  what 
they  stand  indebted  to  you  ;  and  the 
CrcditQr  is  the  discharge. 


# 


[5 


Cr  I     D. 


C. 


Ibi9 


35 
Contra  Cr. 

By  Balance,  remains  2  hhds. 


Dr 


D. 


Contra  Cr. 
By  Balance,  remains  due  to  me     - 


'Note.  When  the  Debtor  side  of  ac- 
compts  belonging  to  men  exceeds  then 
the  balance  is  due  to  me ;  but  if  the 
Creditor  side  is  most,  the  balance  is  due 
to  him. 


C. 

20 


97 


15 


1S19 


36  [6 

Andrew  Thompson  Dr.     '  ^'^  ^*  (   ^' 


Jan.  22   To  Cash,  len,t  to  him 


Jan.  26 


Bills  Receivable  Dr. 

To  Thomas  Richards,  for  one  drawn 
on  him,  to  be  paid  at  sight 


Bills  Payable  Dr. 


Feb.  5   To  Cash,  paid  John  Forrest  hi?  bill 
drawn  on  me  paj'able  at  sight  - 


20 


20 


00 


00 


10 


00 


1819 


37 

Contra  Cr. 
By  Balance,  remains  due  to  me 


Dri 


Contra  Cr» 
Jan.  28  By  Cash,  received  the  bill 


Jan.  2 


D. 


20 


C. 

00 


m 


Contra  Cr. 

By  John  Forrest,  for  a   bill    drawn 
on  me         -         .         .         - 


20 


00 


40 


00 


Dd 


3H 


[7 


U119  j        Profit  and  Loss  Dr. 

Feb,  9  To  Cash,  paid  John  Forrest  a  quar- 
ter's  interest         .         -         - 
10  To  Ca«h,  given  A  B  Esq's  serrants 
13  To  Cash,  paid  1    month's  household 

j     expenses         -         -         - 
iSjTo  Cash,  paid  my  hook-keeper  one 
quarters    salary,    and   other    ex- 
penses        .         -         -         - 
To    Cash,   paid  for  supporting    the 

poor 
To  Cider,  lost 
To  Stock,  gained  by  trade 


Cr 


D. 


James  Morgan  Dr. 


To  Balance,  remains  due  on  demand     9 


00 
00 

15 


50 


00 


24 


96 


C. 


75 
80 

G7 


75 

87i 
00 

68 


40 


OU 


n 

IS  19 

Feb,  n 
20 


39 
Contra  Cr. 

By  Cash,  won  at  billiarJs 

By  William  Cowley,  gained  by  sell- 

ing;  my  goods  at  New- York 
By    Cash,   tor  a  legacy    left  me    by 

my  unele 
By  Hops,  gained 
By  Wine,  gained 
By  Broadcloth,  gaineel    ^    - 
By  Cheese,  gained 


Dr 

D. 

1 

7 

8 

7 

1 

20 

2 

23 

o 

29 

2 

7 

4 

2 

961 

Feb.  8 


Contra   Cr. 
By  Cash,  borrowed 


40 


37^ 

23J 

00 
00 
66 
05 
20i- 


52-1. 


00 


40 


rs 


isid 


eh.  n 


20 


Feh.  23 


Voyage  to  New-York  Dr. 

To  Sundry  Accounts,  as  per  Journal, 
To  Cheese,  for  2  cvvt.  of  Cheshire 
To  Cash,  paid  freight  and  custom 


William  Cowley  Dr. 

To  Sundry  Accounts,  as  per  Journal, 
To  Voyage  to  New-York 
To  Profit  and  Loss,  gained  by   sell- 
ing goods         -         .         -        , 


Sugar  Dr. 

To  Sundry  Accounts,  as  per  Journal, 
To  William  Cowley,  for  one  chest, 
neat  weight  3  cwt.  2  qrs.  valued  at 
To  Cash,  paid  freight  and  custom 


Cr 

4 
1 

D. 

8 
2 

11 

a 

751 
33i 

09 

8 

7 

8 

1 

11 

7 
18 

09 

231 

321 

15 

2 

18 

871 
45 

321 

• 

{q  41 

1319  Contra  Cr. 


Feb.  20  By  William   Cowley,  who  has   re- 
ceived the  2:oods  sent  thither  - 


Dr 


1^ 


FehT23 


^  Contra   Cr. 

By  Sugar,  received  1  chest,  neat  wt. 

3  cwt  2  qrs.  ji'alued  at     ,    - 
By  Balance,  remains  due  to  me  - 


Contra  Cr. 

By  Balance,  remains  1  chest,  neat  wt. 
3  cwt. 2  qrs.  valued  with  charges  at 


D. 


11 


09 


15 
2 


18 


45" 


32;^ 


18'    32-1- 


Dd  2 


m 


■"^S^ 


42 
1B19  i  Balance   Dr. 

To  Cash,  remaining  in  nvj  hands  - 
To  Hops,  6  bags    remain,  at  10,00 

per  bag         -         -         *         _ 
To  Wine,  remain  2  pipes,  at   65,50 

per  pipe 
To  Broadcloth,  remain  5  pieces,  at 

90,10  per  piece 
To  Thomas  Richards,    remains  due 

on  demand         -         -         -         - 
To  Cheese,  remains  |  a  ton  of 

Gloucester,  at  BO,  00  per  ton  40,00 
"  "-         8  cwt.  of 

Cheshire,  at  05,50  per  ton     26,20 


To  Tobacco,     remains    2  bhds.  at 

39,60  per  hhd. 
To  John  Jones,  remains  due  to  me 
To  Andrew  Thompson,  remains  due 

to  me 

To  William  Cowley,  remains  due  to 

me 

To  Samuel  Taylor,  remains  due   to 

me         -         - 
To  Sugar,  remains  in  my  hands   - 


Cr'j    D. 


These  articles  on  the  Debtor   side  are   the 
several  branches  of  my  present  estate 


1009 

60 

131 

450 

25 

66 

79 

97 

20 

2 

20 
18 

1980 


[9 

c. 

24|- 
00 
00 
50 

75 

20 

20 
15 

00 

45 

71 

321 

5^ 


1819 


4S 
Contra  Cr. 

By  John  Forrest,  remains  due  to  him 

\]y  Richard  Payton,  remains  due  to 

him 

By  James  Morgan,  remains  due  to 

him 
r»v  Stock  for  the  neat  of  my  estate 


Dr      D. 


m 


These  articles  on  thij  Creditor  side  (except 
the  last,  which  is  the  neat  value  of  my 
estate)  are  the  several  debts  I  owe 


10 
17 


7;      40 
1^913 


C. 

00 

50 

00 
03 


1980 


53 


End  of  the  Ledger. 


LIST  OF  AUXILIARY  BOOKS, 

MORE    OR    LESS    NECESSARY     TO    DIFFERENT      KINDS    0 
BUSINESS,  AND    TO    BE    MODIFIED     ACCCfeDlNGLY. 


Cash  Book,  (Ledger-wise)   in  which   receipts  of  monej 
are  entered  on  the  left,  and  payments  on  the  right  hand  page. 
Invoice  Book,  of  all  shipments  out  a»d  home. 
Letter  Book,  containing  copies  of  letters  sent  and  received. 
Bill  Book,  of  exchange  and  acceptances. 
House-Expense  Book. 
Charges-on-Merchandise  Book. 
Till  Book^  in  which  Retailers  enter  their  daily  cash  sales. 


WASTE-BOOK 

AS    AN 

EXAMPLE  FOR   PRACTICE, 


4B 


Boston,  March  15M,  1819- 


Bought  of  Henry  Gerry  10  pipes  of  brandy, 

at  120,00  per  pipe 
Paid  in  cash  ,  .  .     150,00 

Gave  a  bill  on  John  Jones  for         .       97,15 
Due  at  3  months  .  -     .      952,85 


-20th.- 


Borrowed  of  John  Jackson,  for  3  months,  at 
5  percent.  -  -  -         - 


--24th~ 


Paid  James  Burrows  in  full  for  fish 

21 th 


Bartered  with  James  Dobson, 

6  cwt  of  Gloucester  cheese,  at  5,00 

per  cwt.  -  -  -        30,00 

2  hhds.  of  tobacco,  at  42,00  per  hhd.     84,00 


For  6  barrels  of  cider,  at  3,00  per 
bj^rrel  -  -  - 

14  do.  of  strong  beer,  at  7,00 


18,00 
98,00 


-30th- 


[Received  in  full  for  wine,  of  John  Fenton 


I  John  Jones  is  deceased,  and  has  left  me  a 
leeracy,  payable  by  his  executor,  John 
Palmer  -  .  .  « 


D. 


O. 


1200 


400 


00 


00 


10 


00 


114 


116 


70 


200 


00 


00 


00 


00 


19 


JJoston,  Jpril  3d,  1819. 


D.  !  r 


iThomas  Richards  has  faileil,  and  I  havci 
i  compounded  my  debt  ol  25,76  with'  him.i 
Composition  received  is  -  14,50; 

j Discount  is  -  -  -:        l\^b\ 


-6(h- 


Paid  a  quarter's  house-rent,  due  April  1st 
9th V 


Sold  Edward  Nelson  20  quintals  of  cod  fish, 

at  3,50  per  quintal. 
Received  in  cash  -  -  15,25 

His  bill  on  John  Burrows         -         -     54,75 


-15th- 


Bou2:ht  for    cash    20  pieces  of  nawkeen,  at 

1,00  per  piece  -  -  20,6(' 

5  pieces  of  moreen,  at  7,00         -     -      35,00 


.■:d,  i  7o 


25      GO 


70 


Received   from   on    hoard     the    Friendship* 

Isaac    Watson    masior,    from    Hamburgh. 

shipped,   by    my  order,  by   Herman    Vai 

Beck,  merchant  tlierp, 
GO    pieces  of  Russia  sheeting,  at  14,00    per! 

piece  -         ,    -  .         '  840,001 

20  do    platillas,    at  7,00  per  piece     MO^OOJ 
30  pair  of  silk  hose,  at  1,25  per  pair     37,50i 


1 


Amount  carried  forward^         1 0 1 7,50! 
E  K 


00 


00 


50 


Boston,  Jpril  20tk,  1819. 


Amount  brought  forivard^  1 0 1 7 ,5o 

Charsfes  at  shipping:,  per  invoice     -  10,00 
Freight,  custom,  and  other  charges 

here             -             -             -  100,50 


^.24th- 


R.cceive<]   of  John  Burrows,  in  full  for   Ed- 
;vard  Nelson's  bill      -       - 


--2eth- 


Sold  for   cash  10  pieces  of  nankeen,    at  1,25 
per  piece  -  -  -         - 


►  -.26th- 


Bong;ht  of  John  lliirrows  40  barrels  of  flour, 

at  10,00  per  barrel. 
Paid  in  cash  -  -  -        100,00 

Gave  a  bill  on  John  Palmer  -         150,00 

Due  at  3  months  -  -  150,00 


-2Sth- 


Scnt  as  an  adventure  to  the  Havana,  per 
Recovery,  Joseph  Jiollin  master, 
.,  ;.  ^ncd  to  said  Rollin  for  sales  and  re- 
i  turns,  the  goods  following*,  viz. 
[20  bhls.  of  tlour,  at  10,00  per  bbl.  200,00 
,30  pieces  Russia  sheeting,  at  16,00 
j      per  piece  -  -         '    -     480,00 

jlO  do.  nankeen,  at  1,25  -.        -    12,50 

'Charges  at  shippii^g  -  -       45,50 


%. 


51 


Boston,  April  ^0,  1819. 


D.     C. 


Bought   of  James   Knight   50  pieces  of  Irish 

linen,    25  yards    each,  at  8,50  per  piece 
Paid  in  cash  -  -  -      41,00 

Due  at  90  days  -  -  381,00 


Sold    for    cash   5  barrels    of  flour,  at    1 2,0; 
per  barrel  -  .  - 


-May  1st 


jCharges  on  my  trade  last  month 


-ad- 


Received    from  on  board  the  Pollj^,    James 

Smith    master,    from    Baltimore,   shipped 

by  John  Flint  on  my  account, 

75    barrels  oi  flour,  at  7,50    per    barrel,   as 

per  mvoice  -  -  562,50 

20    bu>h.  of  corn,  at  50  cts.  per  bush.  10,00 

Received  in  cash  -  -  105,30 

Paid  freight  -  -  -      75.00 


The    above    is    the  neat  proceeds  of  my    3 
bales  of  India  cottons,  as  per    John  Flint- 
account  of  sales. 

Sold  for  cash  3  barrels  of  cider,  at   5,50  pei 
barrel  -  _  .  . 


425 


GO 


40 


00 


00 


OQ 


832 


80 


IC  50 


Boston,  May   Gth,  1819. 


Bought  of  William  Lamsoii  4  bbls.  of  strong- 

beer,  at  8,00  per  bbl. 
Paid  him  in  cash  -  -  . 


^._8th- 


S old  for  cash  10  barrels    of  flour,  at     12,00 
per  barrel  -  .  . 


-^9th- 


;  Gave  in  charity 


-10th- 


iccepted  William  Lamson'S  bill  on   me,  pay- 
able at  3  days'  sight,  for 


— lltb 


Paid  John  Burrows 
Abated  me  for  cash 


47,50 
^,50 


— 13th- 


D.  i  C. 


32    00 

75,   00 


120    00 


CO 


150,  00 


Paid    William  Lamson  in  full  for  his  bill  on 


-14th- 


50 


150 


00 


00 


Sold  John  Foot  50  barrels  of  flour,    at  12,C0 
per  barrel 


Received  in  pnrt,  cash 

I  His  promissory  note,  payable  in  7 

I      davs  _  .  - 


250.00 


COO 


600 


00. 


00 


Boston,  May  ^Gth,  18 1^  D. 

Bought  of   William  Gordon    40    pieces    ofl 
baadannoes,  at  5,01)  per  piece     -     200,00 

20  do.  pulicat  handkerchiefs,  at  G,00 

per  piece  -  -  -     120,00] 

30  do.  India  chintz,  at  3,50  per  piece  105,00| 


C. 


Paid  in  cash 


50,00 


425 1 


10    bbls  of  ilonr,  at  12,00  per  bbl.        120,00; 
Due  in  30  days  -  -       -      255,00| 


~17th. 


[    have  drawn  a  bill    on  John  Foo.t,    payjible| 
at  sight,  ibr  -  «   .  -  i 


425 


125 


00 


00 


00 


John  Foot  has  paid  the  bill  I  drew  on  him 


12c 


.»l| 


Sold    for  cash  15  pieces   of  India  chintz,    at 
5,00  per  piece  _  -  . 


-18ih- 


Sold    for    cash  30  pieces  of  bandannoes,    af 
7,00  per  piece  .  -  - 


-20ili- 


Bartered  with  Joseph  Mann, 

5  pieces  of  Russia  sheeting,  at  20,00 

per  piece  .  -  .     100,00 

3  do.  moreens,  at  10,00         -        -       30,00 


75'  CO 


210    00 


130     00 


Ee  2 


54 


Boston,  May  20th,   1819. 


tor — 

1  hogshead  of  sugar,  71  cvvt.  at  8,00 

per  cwt.  -  .  -  -         60,00 

200  lbs  of  coffee,  at  0,25  per  lb.     -       50,00 
20  pair  of  shoes,  at  0,75  per  pair     -      15,00 


-21st- 


Received  of  John  Foot  in  full  for  flour 

22d 


Shipped  for  Sumatra,  in  the  ship  Britain 
Gapt.  Colby,  consigned  to  him  for  sales 
and  returns,  5  pipes  of  brandy,  at  120,00 
per  pipe  .  *  -  > 


26th- 


Paid  premium  for  insurance    on  600  dollars 
on  voyage  to   Sumatra,    premium    at    12| 
per  cent.  -  -  - 


-27tli- 


(Paid  James  Morgan  in  full 


D. 


C. 


125 


125 


00 


00 


600 


-2Sth- 


Paid  William  Gordon 

30th- 


'iil'l  for  house  expenses 


End  of  the   Waste-Book. 


75 


40 


255 


00 


00 


00 


00 


50 


A 

JOURNAL  &  LEDGER 

BY  SINGLE  ENTRY. 


56 


It  having  been  sufi^g^estcd  that  an  elucidation  of  the  most 
approved  mode  of  Book-Keenin2f  by  Singlr  Entry  wouhl  he 
useful,  the  first  fVaste  Book  is  here  journalized^  and  posted 
into  Ledger^  upon  that  system. 

The  utmost  simplicity  and  plainess  areused_^in  this,  as  in 
the  former  set  of  books. 

A  Cash'f3o()k^  separately,  may  be  used,  or  some  pages  in 
the  Ledger  may  be  appropriated  for  that  purpose. 

In  real  business,  som;?  or  all  the  other  auxiliary  hooks  will 
be  needed.     Their  use  has  been  already  explained. 

When  an  account  is  Debtor,  the  n  ord  '^  Dr."  in  the  Jour- 
nal entry  follows^  when  it  is  Creditor,  '•'  Cr."  goes  before,  the 
name  of  the  account.  This  is  an  additional  guard  against 
posting  on  the  wrong  side. 

Sometimes  a  single  transaction,  or  Waste  Book  entry,  will 
require  two  Journal  entries  :  for  instance.  Stock  and  Cash 
transactions,  which  accounts,  if  the  hooks  are  properly  kept 
;md  adjusted,  must  necessarily  partake  of  the  Double-Entry 
nature. 

This  Ledger  being  paged  like  that  of  the  Double- Entrij 
one,  the  same  alphabet  answers  for  both. 

Let  the  Waste>&ook  be  carefully  examined  before  jour- 
nalising, and  the  Journal  compared  with  the  Waste-Book 
before  posting  into  the  Ledger  ;  and  again,  the  Ledger  com- 
pared with  the  Journal  after  posting. 

It  may  he  well  here  to  observe,  that  charges  should  be 
made  as  soon  as  possible,  and  in  a  plain  and  full  manner. 
Also,  that  receij)ts  should  be  taken  for  all  payments  on  ac- 
count ;  and  a  person  making  a  payment  on  a  note  should  sec 
the  same  properly  endorsed. 


JOURNAL.     (Single  Entry.)  57 

Boston^  January  \st^  1819.         I  ^-      C. 


Cr.     Stock, 

By  Sundries,  per  Inventory  in  Waste 


Stock  Dr. 

—  iTo  buntlries,  per  ditto,  ditto. 

I ct 


1 


Cash  Dr. 
To  Stock,     per  ditto,  ditto. 

Note.  This  is  to  be  posted  into  the  Cash-Book 
or  the  Cash  Acct.  m  the  Ledger  ;  and  it  partakes  of 
the  Double-Entry  nature. 


1918 


CO 


1000 


Cr.     Cash, 

By  Cheese,  \  ton  Ciieshire 

3d. 


Cr.     Cash, 

By  Cider,  paid  in  part  for  4  hhds. 


Cr.     Richard  Payton, 
By  Balance  Cider,  due  1  mo. 


jtii. 


Cr.     Samuel  Taylor, 

By  2  hhds.  Tobacco,  3  nios. 


■7th.. 


Cash     Dr. 

To  4  ba;-;  \\o\)<.  sold  J.  Willinnfis 
10th. 


35 


GO 


00 


00 


63 


Casli     Dr. 

To  rcc'd  of  S.  Taylor  in  part,  2  pipos  Wine'      50 


20 


00 


38 


JOURNAL.     (Single  Entry.) 
Boston  J  Jamianj  lOthj  1810. 


Samuel  Taylor     Dr. 

To  Balance,     ditto,     ditto,  demand 
- 1  5tlu-^ 


John  Jones     Dr. 

To  1  piece  Broadcloth,  1  month 

[9th 


Note.     The   barter  of  cider  for  cheese,  in  Single 
Bart.   Entry   Book-Kceping,  need  not  be    Journalised,  but 


Mem. 


Poitcd  immediately  into  a  Barter  Book,  or  memoran- 
dum. 


.22d- 


Andrew  Tliompson    Dr. 

Vo  Cash  lent,  demand 


Cr.     Cash, 

By  lent  Andrew  Thomnson,  as  ahove 
, ^>6'th 


Cr.     Thomas  Richards, 

By  BiH  drawn  at  si2;ht 

._! J^  S  th 


Bill 


Note.      As   Thomas    Richards  has   before   been 


Book  ^^^^  ^''^'  ^^^i^  amount    post  this   pajinent   into    Bili 
Book  or  Memorandum. 


.^'.'tb. 


J*  hn  Forrest    Dr. 

Fo  Bill  drawn  at  sight 
Fob.    5th-.- 


Bill         Note.     This  entry  need  not    be  journalised  ;  post 
Book  Idirectly  into  Bill  Book  or  Memoraiidum, 


JOURNAL.      (Single  Entry.) 


dd 


1 
H.Ex 


Boston^  February  Sth^  1819. 


Cash    Dr.    f^^*  nature  of  Double   E7itnj\ 
To  James  Morgan,  borrowed 


Cr.     James  Morgan, 

By  Cash,  borrowed 
Otb 


D. 


40 


C. 


00 


Cr.     Cash, 

By  Interest,  paid  J.  Forrest 

10th 


Cr.     Cash, 
By  given  A.  B's  Servants         -         -         - 

Note.     Post  this  also  into  House  Expense  Book. 

1 1  th 


\0 


00 


Ch. 
Mer 


Cash     Dr. 

To  won  at  Billiards 
1  Sth. 


Cr.     Cash, 
By  Household  Expenses,  last  month 

Note.     This  may  be  supposed  to  be   taken   from 
House-Expense  Book. 


>th. 


Cr.     Cash, 

By,  paid  Book  keeper  1  quarter 

Note.     Post  this  also  into  Charges-on-Merchan- 
dize  Book. 


,.-16th. 


75 


80 


15 


371 


67 


5(' 


75 


Wm.  Cowley,  N.  York,  Dr.  for  sale, 

2  cwt  Cheese         -         .         .         -         - 


7^>» 


60  JOURNAL.     (Single    Entry.) 

Boston^  February  1 6/A,  1819. 


Cr.  Cash, 

By  paid  freight,  he.  on  the  above 

-liJOth- 


William  Cowley     Dr. 

To  amount  Cheese  sold         -         -       21,07| 
Deduct  former  debit     -       B,75i 
'-^  charges        .-         2,75 

11,501 

23d 

Cr.     William  Cowley, 

By  1  chest  Sugar         .         >         -         - 


Cr.     Cash, 

By  paid  Freight  and  Custom  on  ditto 
25th- 


Cash  Dr. 

To  Leiracy  left  by  uncle 
__-! ! 27th-. 


Cr.     Cash, 

By  paid  Poor 


Note.  When  you  post  into  Ledger,  if  it  is  a  Cr. 
entry,  put  into  the  marsrin  of  the  Journal  *he  p-^.i  e  of 
the  account  in  the  Ledger,  -wi'};  a  snail  ii'  e  over  ii  ; 
if  it  is  a  Dr  entry,  put  the  small  line  under  it. 


End  of  the   Journal. 


THE 

LEDGER. 


^^  In   the  following  Ledger  the  entriejs  are  posted   verv  ' 
concisely.     In  real    transactions  they  may  be  as  full    as    the 
room,  convenience  and  particular  business  of  the  person  may 
allow  and  require. 


F  F 


G2 


LEDGER.     (Single  Entry.) 


b 


1819 

Dr.    Stock 

D. 

./«n.  1 

To  Sundries,  per  Journal 

60 

Dr.  Cash 

Jan.  1 

7 

10 

28 

Feb.  8 
11 
25 

To  Stock  on  hand 

To  Hops         -         -         -         - 

To  Wine         -         -         -         - 

To  Bill,  T.  Richards 

To  James  Morgan         -         -         - 

To  Billiards         .... 

To  Legacy         .... 

1000 
63 
50 
20 
40 
7 
20 

120! 

[Page  3] 

Dr.      Thomas  Richards 

/an.  1 

To  Stock,  on  demand 

45 

c. 

00 


0§ 
00 
75 

00 
90 
37J 
00  "^ 


124 


7g 


11 


[Page  3] 

Jan.  26 
Feb.  27 


LEDGER.     (Single  Entry) 
Contra  Cr. 


&o 


Contra  Cr. 

By  Cheese         .... 

By  Cider,  part 

By  A.  Thorn psoii 

By  Bill,  J.  Forrest 

By  Interest         .... 

By  Expenses         .         .         .         . 

By  ditto         .... 

By  Charges,  merchandise 

By  Freight  and  Custom 

By  ditto,  Sugar 

By  Poor         

By  Balance  on  hand,  for  new  acct. 


Contra  Cr, 

By  Bill,  on  sight 
By  Balance,  remains  due  me  for  new 
acct         .         .         . 


D. 
1948 


32 
25 

20 
40 


15 

50 

2 

1009 
1201 


20 
25 
45 


'U 


1819 

Jan.  29 
Feb.  27 


Jan.  10 


kf  AGC  4] 

Feb.  27 


Ta/i.  15 


LEDGER.     (Single  Entry.) 
Dr.     John  Forrest 

To  Bill,  at  sight 

To  Balance,  due  him  for  new  acct. 


[3 


D. 

40 
10 

50 


OQ 
00 

00 


^Dr.     Samuel  Taylor 

To  Wine^  on  demand 


109 


91 


Dr.     Richard  Pay  ton 

To  Balance.,  due  him  for  new  acct. 


17 


60 


Dr.     John  Jones 

To  Broadcloth,  I  mo. 


97 


15 


3] 


1819 
Jan.  1 


LEDGER.     (Single  Entry.) 
Contra  Ci\ 
By  Stock,  secured  by  bond 


Jan.  1 
5 

Feb.  27 


[Page  4] 
Jan.  3 


(Page  5] 
Feb.  27 


Contra     Cr. 

By  Stock,  due  him 

By  Tobacco,  2  hhds. 

By  Balance,  due  me  for  new  acct. 


Contra  Cr. 
By  Cider,  1  mo. 


Contra  Cr. 
By  Balance,  due  me  for  new  acct. 

Ff2 


D. 


60 

50 


10 

GO 

79 

20 

20 

71 

109 

91 

17 


97 


65 

C. 

00 

00 


5d 


15 


►6 

LEDGER.     (Single  Entry.) 

CJ 

1819 

Dr.  Andrew  Thompson 

D. 

c. 

Jan.  22 

To  Cashv  lent 

20 

00 

[Page  7] 

Dr.     James  Morgan 

Feb.  27 

To  Balance,  due  him  for  new  acct. 

40 

00 

• 

[Page  8] 

Dr.     William  Cowley 

Feb.  16 

50 

To  Cheese, /or  5a/c 
To  ditto,  balance 

8 
■    9 

751 

571 

f 

18 

33 

S] 


1819 
Feb.  27 


[Page  7] 
Feb.  8 


[Page  8] 

Feb,  23 
27 


[Page  9] 


LEDGER.     (Single  Entry.) 
Contra  Cr. 
By  Balance,  due  me  for  new  acct. 


67 


Contra  Cr. 

By  Cash,  borrowed 


Contra  Cr. 

By  Sug-ar         .... 
By  Balance,  due  me  for  new  acct. 


Balance   acct.  same   as  in  Double    Eedger, 
Both  should  be  dated  Feb.  27, 1819. 


D. 

20 

C. 

OQ 

40 

00 

15 


18 


33 


JAMES  R.  BUFFUM 

(Proprietor  of  Walsh's    Mercantile  Arithmeti«) 
i  Keeps  constantly  for  sale^  at  his 

NAVIGATION  AND  COMMERCIAL  BOOK:STORE, 
CEJSTTRAL  BUILDLVG,  ESSEX  STREET,  SALE^jj., 

A    GENERAL   ASSORTMENT  OF 

CKikXtTSy  ^or  the  navigation  of  every  sea,  parti- 
•ularly  Lambkrt's  late  and  improved  Charts  oi  the  American 
Coast,  viz.  Massaciiusetts  Bay,  on  a  scale  of  12  inches  to  a 
degree  ;  Nantucket  Shoals  and  George's  Banks,  7  inches  to 
a  degree  ;  Coa«t  of  Connecticj^t,  4^c.  extending  from  Mon- 
tock  Point  to  Chincoteague  Shoals,  on  the  same  scale  ;  the 
Coast  from  Nova-Scotia  to  the  Chesapeake ;  Chesapeake 
Bay;  North  and  South  Carolina?  the  Missisippi  River;  and 
the  Bahama  Banks,  Islands,  &;c.     Also^ 

QXTADRAJNTTSp  Telescopes,  cases  of  Mathematical 
Instruments,  Gunter's  Scales,  Protractors,  steel-jointed  and 
oommon  Dividers,  Parallel  Rules,  Thermometers,  &,c. 

BO^CI7DITCK'S  Practical  Navigator,  teaman's 
Daily  Assistant,  Searjien's  Journals,  Nautical  Almanacks, 
Cargo  Books,  Shipmaster's  Assistant,  Abbot  on  Shipping. 

BLXriffT'S  American  Coast  Pilot;  the. Oriental  Nav- 
igator, or  Sailing  Directions  to  and  from  thfe  Eaet-lndies  ; 
Sailing  Directions  for  the  Coast  of  Africa,  North  Sea, 
Baltic,  West-Indies,  and  Ohio  and  Missisippi ;  Treatise  on 
the  Navigation  of  St.  Domingo,  with  sailing  directions  for 
the  coasts,  bays  and  harbours  thereof. 


COMMISRCXAK    DICTX09JA11Y,    »i* 

tionary  ot  Merchandise,  L  reatise  on  the  law  relative  to 
Principals,  Agents,  Factors,  Auctioneers  and  Brokers,  Oliver's 
Practical  Convejancino;,  Marshal  on  Insurance,  Annerican 
Trader^s  Compendium,  Brice's  Revenue  Laws,  Jackson's 
Commerce  of  the  Mediterranean,  Beaujour's  Commerce  of 
Greece,  System  of  Exchange  with  all  parts  of  the  world, 
India  Directory  for  purchasing  Drugs  and  Spices,  Merchant 
and  Shipmaster's  Ready  Calculator,  Cieavland's  Exchange 
Tahles. 

TaARlTSBTL'S  DICTIOSffAHY,  Malham'e 

Naval  Gazetteer,  Worcester's  Gazetteer,  Brookes's  do. 
Morse's,  Oummings's,  Adams's,  Dwight's,  Parish's,  Pinker- 
ton's,  Mann's,  Goldsmith's,  and  other  Geographies. 

Art  of  Mast-Making,  with  a  book  of  plates, 

Art  of  Sail-making,  Ship-builder's  Assistant,  Pakenham's 
Substitute  Tor  a  Lost  Rudder. 

SOOK-KEEFIMa.  Merchant's  System,  inv 
proved  upon  Turner;  Turner's  and  Shey's  System;  Perry's 
Man  of  Business. 

A  SKTJS'^DSr  SirST£2M[  of  Mercantile  Arithmetic, 
adapted  to  the  Commerce  of  the  United  States^  in  its  Domes- 
tic and  Foreign  Relations;  with  Forms  of  Accounts,  and  oth- 
er VVritmgs  usually  occurring  in  trade.  By  Michael  Walsh, 
A.  M.  This  work  is  strongly  recommended  by  the  first 
Merchants  in  the  Siaie^  "  as  better  calculated  than  any  yet 
published  to  fit  youth  for  the  Compting-house,  and  from  the 
useful  commercial  information  it  contains,  extremely  well 
adapted  to  assist  the  merchant,  the  mariner  and  the  trader, 
in  their  various  occu[)ations."  To  which  is  annexed,  a  Sys- 
tem of  Book-Keeping.  Also^  Temple's,  Adams's,  VVelsh'Sj 
Daboll's,  and  other  Arithmetics. 

Histories,  Voyages,  Travels^  Novels,  and  a 

great  variety  of  Books  of  instruction  and  amusement,  loaned 
on  resonable  terms. 

S!1B£!^S,  I'lrge  and  small,  Testaments,  Psalm  aB^ 
Hymn  liooks,  and  all  kinds  of  School  Books. 


STATIONARY,  &C.  ^^riting-,  Wrapping-,  Cart- 
ridge,  L«'g-iiook,  iilu( ,  Mari  ie,  Wove,  Hot  Pressed,  Gilt, 
Letter,  Drawing  and  Ruled  PAFLR,  of  every  size  and  qual- 
ity, European  and  American.  Qnilis,  Ink,  Inkpowder,  Wa- 
fers, sealing  Wax,  Elastic  Gum,  Black  Sand,  Sponge,  India 
Ink,  Paint  Boxes,  Durable  Ink  tor  marking  linen  with  a  pen  ; 
Inkstands  for  tlie  compting  house,  schools,  portable  writing 
desks,  and  the  pocket,  band  Boxes,  Penknives,  Gutteaux, 
Pencils,  Pencil  Gases,  Shaving  Soap,  Slates  and  Pencils, 
Purses,  Folding  Knives,  Pocket  Rules,  Stationers'  Tape, 
Scissors,  Tooth,  Head,  and  Glothes  Brushes,  Gourt  Plaister, 
4^c. 

Merchants'  Account  Books,  and  Blank  Books 

•f  various  kinds,  Giphermg  and  Writing  Books,  Ladies'   and 
Gentlemen's  Pocket  Books,  Memorandum  Books,  &c. 

Blanks. — Commercial,  Nautical,  Notarial,  Jus- 
ticiary, Military,  &z.c   he.  kc.     Printed  Note  Books. 

Music^  Musical  Instruments,  Music  Paper,  and 

a  g^eneral  Stock  for  a  Book  and  Stationary  Store. 


ALL  KINDS  OF 

H^o^  $t  S^%^  priif  ting 

HANDSOMELY    EXECUTED 
BY 

Jfohn  D.  Oushingj 

f>NE  DOOR  WEST  OF  SALEM  HOTEL,  ESSEX  STREET,  SALEM, 
ORDERS  LEFT  AT  THE  BOOK-STORE  OF 

JAMES  R.  BUFFUM, 

WUX    BE    IMMEDIATELY    ATTENDED    TO, 


\y  1 


A  new  syistem  of  mer- 
cunt lie  ar 


ithmetio 


B2^ 


t, 


■^'' 


17283911 


^/^  lot 


THE  UNIVERSITY  OF  CAUFORNIA  UBRARY 


-1^ 


^■■m.. 


r^ 


